Deck 7: Rational Expressions and Functions

Question 1

Find all numbers not in the domain of the function

- $f(x)=\frac{8}{x-3}$

A) None
B) 0
C) 3
D) -3

Answer 1

3

Question 2

Find all numbers not in the domain of the function

- $f(x)=\frac{2}{x+9}$

A) 0
B) None
C) -9
D) 9

Answer 2

-9

Question 3

Find all numbers not in the domain of the function

- $f(x)=\frac{x-7}{2}$

A) 0
B) None
C) -7
D) 7

Answer 3

None

Question 4

Find all numbers not in the domain of the function

- $f(x)=\frac{x-7}{5-x}$

A) 5,7
B) None
C) -5
D) 5

Question 5

Find all numbers not in the domain of the function

- $f(x)=\frac{x^{2}-64}{x^{2}+4 x-32}$

A) $8,-8$
B) $8,-4$
C) 0
D) $-8,4$

Question 6

Find all numbers not in the domain of the function

- $f(x)=\frac{x^{2}-16}{x^{2}+4 x-32}$

A) $4,-4$
B) 0
C) $-4,8$
D) $4,-8$

Question 7

Find all numbers that are not in the domain of the function. Then give the domain using set notation.

- $f(x)=\frac{4}{x-2}$

A) $2 ;\{x \mid x \neq 2\}$
B) $-2,2 ;\{x \mid x \neq-2,2\}$
C) $-4 ;\{x \mid x \neq-4\}$
D) none; $(\infty, \infty)$

Question 8

Find all numbers that are not in the domain of the function. Then give the domain using set notation.

- $f(x)=\frac{x+1}{3 x+4}$

A) $-\frac{4}{3} ;\left\{\left\{x \mid x \neq-\frac{4}{3}\right\}\right.$

B) none; $(\infty, \infty)$

C) $-\frac{4}{3},-1 ;\left\{x \mid x \neq-\frac{4}{3},-1\right\}$

D) $\frac{4}{3} ;\left\{x \mid x \neq \frac{4}{3}\right\}$

Question 9

Find all numbers that are not in the domain of the function. Then give the domain using set notation.

- $f(x)=\frac{x^{2}-10 x}{2 x}$

A) $\frac{1}{2} ;\left\{x \mid x \neq \frac{1}{2}\right\}$

B) $0 ;\{x \mid x \neq 0\}$

C) $2 ;\{x \mid x \neq 2\}$

D) 0, $10 ;\{x \mid x \neq 0,10\}$

Question 10

Find all numbers that are not in the domain of the function. Then give the domain using set notation.

- $f(x)=\frac{12}{x^{2}+7 x-18}$

A) $-9,2 ;\{x \mid x \neq-9,2\}$

B) 0 ; $\{x \mid x \neq 0\}$

C) $-2,9 ;\{x \mid x \neq-2,9\}$

D) $0,-9 ;\{x \mid x \neq 0,-9\}$

Question 11

Find all numbers that are not in the domain of the function. Then give the domain using set notation.

- $f(x)=\frac{2 x+18}{3 x^{2}-6 x-9}$

A) $-3,1 ;\{x \mid x \neq-3,1\}$

B) $\frac{1}{3},-1 ;\left\{x \mid x \neq \frac{1}{3},-1\right\}$

C) $-9,-1,3 ;\{x \mid x \neq-9,-1,3\}$

D) $3,-1 ;\{x \mid x \neq 3,-1\}$

Question 12

Find all numbers that are not in the domain of the function. Then give the domain using set notation.

- $f(x)=\frac{x^{2}+x-6}{2 x^{2}-9 x-5}$

A) $\frac{1}{2},-5 ;\left\{x \mid x \neq \frac{1}{2},-5\right\}$

B) $-\frac{1}{2}, 5 ;\left\{x \mid x \neq-\frac{1}{2}, 5\right\}$

C) $-3,2 ;\{x \mid x \neq-3,2\}$

D) $-2,5 ;\{x \mid x \neq-2,5\}$

Question 13

Find all numbers that are not in the domain of the function. Then give the domain using set notation.

- $f(x)=\frac{2 x+22}{x^{2}-1}$

A) $1 ;\{x \mid x \neq 1\}$

B) none; $(\infty, \infty)$

C) $-1,1 ;\{x \mid x \neq-1,1\}$

D) $-11,-1,1 ;\{x \mid x \neq-11,-1,1\}$

Question 14

Find all numbers that are not in the domain of the function. Then give the domain using set notation.

- $f(x)=\frac{15 x^{2}-2 x+1}{225 x^{2}-169}$

A) $\frac{15}{13}, \frac{15}{13} ;\left\{\left\{x \mid x \neq \frac{15}{13},-\frac{15}{13}\right\}\right.$

B) $\frac{13}{15} ;\left\{x \mid x \neq \frac{13}{15}\right\}$

C) $\frac{169}{225}, \frac{169}{225} ;\left\{x \mid x \neq \frac{169}{225},-\frac{169}{225}\right\}$

D) $\frac{13}{15}, \frac{13}{15} ;\left\{x \mid x \neq \frac{13}{15},-\frac{13}{15}\right\}$

Question 15

Find all numbers that are not in the domain of the function. Then give the domain using set notation.

- $f(x)=\frac{x-3}{8}$

A) $8 ;\{x \mid x \neq 8\}$
B) $0 ;\{x \mid x \neq 0\}$
C) $3 ;\{x \mid x \neq 3\}$
D) none; $(-\infty, \infty)$

Question 16

Find all numbers that are not in the domain of the function. Then give the domain using set notation.

- $f(x)=\frac{x-9}{x^{2}+9}$

A) none; $(-\infty, \infty)$
B) $-9,9 ;\{x \mid x \neq-9,9\}$
C) $9 ;\{x \mid x \neq 9\}$
D) $-9 ;\{x \mid x \neq-9\}$

Question 17

Tell whether or not the rational expressions are equivalent.

- $\frac{a-b}{a^{2}-b^{2}}, \frac{1}{a+b}$

Question 18

Tell whether or not the rational expressions are equivalent.

- $\frac{x^{2}(x+1)}{x(x-1)}, \frac{x(x+1)}{x-1}$

Question 19

Tell whether or not the rational expressions are equivalent.

- $\frac{\mathrm{a}^{2}-\mathrm{b}^{2}+\mathrm{c}^{2}}{\mathrm{~b}-\mathrm{c}}, \frac{\mathrm{a}^{2}-\mathrm{b}^{2}+\mathrm{c}^{2}}{\mathrm{c}+\mathrm{b}}$

Question 20

Tell whether or not the rational expressions are equivalent.

- $\frac{18 x^{2} y^{4}}{36 x^{3} y^{2}}, \frac{2 y^{2}}{4 x}$

Question 21

Tell whether or not the rational expressions are equivalent.

- $\frac{-2 x^{3}+7 x^{2}+15 x}{x^{2}-8 x+15}, \frac{(-x)(2 x+3)}{x+3}$

Question 22

Tell whether or not the rational expressions are equivalent.

- $\frac{4 \mathrm{~m}^{5}}{8}, \frac{\mathrm{m}^{5}}{4}$

Question 23

Tell whether or not the rational expressions are equivalent.

- $\frac{5 m+5}{m^{2}-1}, \frac{5}{m-1}$

Question 24

Tell whether or not the rational expressions are equivalent.

- $\frac{x-2}{2-x}, \frac{1}{x-2}$

Question 25

Tell whether or not the rational expressions are equivalent.

- $\frac{a c+a d-b c-b d}{a b+a c-b^{2}-b c}, \frac{c+d}{b+c}$

Question 26

Tell whether or not the rational expressions are equivalent.

- $\frac{(3-m)(4-n)}{(m-3)(4+n)}, \frac{3-m}{m+3}$

Question 27

Express the rational expression in lowest terms.

- $\frac{30 m^{4} p^{2}}{6 m^{8} p}$

A) $5 \mathrm{mp}$

B) $\frac{5 p}{m^{4}}$

C) $\frac{5 m^{4}}{p}$

D) $5 m^{4} p^{2}$

Question 28

Express the rational expression in lowest terms.

- $\frac{(y+2)(y-6)}{(y-6)(y+9)}$

A) $\frac{y+6}{y+3}$

B) $\frac{2 y-6}{2 y+3}$

C) $\frac{y+2}{y+9}$

D) $\frac{y-2}{y-9}$

Question 29

Express the rational expression in lowest terms.

- $\frac{a^{2}-6 a}{(a+2)(a-6)}$

A) $\frac{a-6}{a+2}$

B) $\frac{a^{2}}{a+2}$

C) $\frac{a}{a+2}$

D) $\frac{1}{a+2}$

Question 30

Express the rational expression in lowest terms.

- $\frac{4 x+2}{20 x^{2}+22 x+6}$

A) $\frac{4 x}{5 x+3}$

B) $\frac{4 x+5}{5 x+22}$

C) $\frac{4 x+2}{20 x^{2}+22 x+6}$

D) $\frac{1}{5 x+3}$

Question 31

Express the rational expression in lowest terms.

- $\frac{y^{2}+9 y+20}{y^{2}+12 y+32}$

A) $\frac{9 y+5}{12 y+8}$

B) $\frac{y+5}{y+8}$

C) $\frac{9 y+20}{12 y+32}$

D) $-\frac{y^{2}+9 y+20}{y^{2}+12 y+32}$

Question 32

Express the rational expression in lowest terms.

- $\frac{y^{2}-3 y-18}{y^{2}+2 y-48}$

A) $-\frac{y^{2}-3 y-18}{y^{2}+2 y-48}$

B) $\frac{-3 y-3}{2 y-8}$

C) $\frac{-3 y-18}{2 y-48}$

D) $\frac{y+3}{y+8}$

Question 33

Express the rational expression in lowest terms.

- $\frac{y^{2}-2 y-15}{y^{2}+12 y+27}$

A) $\frac{-2 y+15}{12 y-12}$

B) $-\frac{y^{2}-2 y-15}{y^{2}+12 y+27}$

C) $\frac{-2 y-15}{12 y+27}$

D) $\frac{y-5}{y+9}$

Question 34

Express the rational expression in lowest terms.

- $\frac{y^{2}+2 y-8}{y^{2}-2 y-24}$

A) $\frac{2 y-1}{-2 y-3}$

B) $\frac{y-2}{y-6}$

C) $\frac{2 y-8}{-2 y-24}$

D) $-\frac{y^{2}+2 y-8}{y^{2}-2 y-24}$

Question 35

Express the rational expression in lowest terms.

- $\frac{5 x-5 y-b x+b y}{5 x-5 y+b x-b y}$

A) Already in lowest terms
B) -1
C) 1
D) $\frac{5-b}{5+b}$

Question 36

Write the rational expression in lowest terms.

- $\frac{5-m}{m-5}$

A) Already in lowest terms
B) 1
C) $-m$
D) -1

Question 37

Write the rational expression in lowest terms.

- $\frac{3 \mathrm{k}-15}{10-2 \mathrm{k}}$

A) 1
B) $-\frac{3}{2}$
C) $\frac{3}{2}$
D) -1

Question 38

Write the rational expression in lowest terms.

- $\frac{(y-3)(y-5)}{(5-y)(3+y)}$

A) $\frac{-(3+y)}{(3+y)}$

B) $\frac{3-y}{3+y}$

C) -1

D) $\frac{(-y-3)}{(3+y)}$

Question 39

Perform the indicated operation and express in lowest terms.

- $\frac{8 p-8}{p} \cdot \frac{7 p^{2}}{9 p-9}$

A) $\frac{9}{56 p}$

B) $\frac{56 p^{3}-56 p^{2}}{9 p^{2}-9 p}$

C) $\frac{56 p}{9}$

D) $\frac{72 p^{2}+144 p+72}{7 p^{3}}$

Question 40

Perform the indicated operation and express in lowest terms.

- $\frac{\mathrm{k}^{2}+12 \mathrm{k}+27}{\mathrm{k}^{2}+18 \mathrm{k}+81} \cdot \frac{\mathrm{k}^{2}+9 \mathrm{k}}{\mathrm{k}^{2}+8 \mathrm{k}+15}$

A) $\frac{1}{\mathrm{k}+5}$

B) $\frac{\mathrm{k}}{\mathrm{k}^{2}+18 \mathrm{k}+81}$

C) $\frac{\mathrm{k}}{\mathrm{k}+5}$

D) $\frac{k^{2}+9 k}{k+5}$

Question 41

Perform the indicated operation and express in lowest terms.

- $\frac{\mathrm{k}^{2}+14 \mathrm{k}+48}{\mathrm{k}^{2}+16 \mathrm{k}+64} \cdot \frac{\mathrm{k}^{2}+8 \mathrm{k}}{\mathrm{k}^{2}-2 \mathrm{k}-48}$

A) $\frac{1}{\mathrm{k}-8}$

B) $\frac{k^{2}+8 k}{k-8}$

C) $\frac{\mathrm{k}}{\mathrm{k}-8}$

D) $\frac{k}{k^{2}+16 k+64}$

Question 42

Perform the indicated operation and express in lowest terms.

- $\frac{2 p-2}{p} \div \frac{5 p-5}{7 p^{2}}$

A) $\frac{14 p^{3}-14 p^{2}}{5 p^{2}-5 p}$

B) $\frac{14 p}{5}$

C) $\frac{10 p^{2}+20 p+10}{7 p^{3}}$

D) $\frac{5}{14 p}$

Question 43

Perform the indicated operation and express in lowest terms.

- $\frac{z^{2}+9 z+14}{z^{2}+13 z+42} \div \frac{z^{2}+2 z}{z^{2}+15 z+54}$

A) $\frac{z+9}{z^{2}+6 z}$

B) $\frac{z+9}{z}$

C) $z+9$

D) $\frac{z}{z^{2}+13 z+42}$

Question 44

Perform the indicated operation and express in lowest terms.

- $\frac{z^{2}+9 z+18}{z^{2}+14 z+48} \div \frac{z^{2}+3 z}{z^{2}+2 z-48}$

A) $\frac{z-6}{z^{2}+8 z}$

B) $\frac{z}{z^{2}+14 z+48}$

C) $\frac{z-6}{z}$

D) z - 6

Question 45

Perform the indicated operation and express in lowest terms.

- $\frac{(x-2)(x+3)}{(x+8)(x-2)} \cdot \frac{(x-9)(x+8)}{(x+3)(x+5)}$

A) $\frac{x+9}{x-5}$

B) $\frac{x-9}{x+5}$

C) $\frac{x+3}{x-2}$

D) $-\frac{x-9}{x+5}$

Question 46

Perform the indicated operation and express in lowest terms.

- $\frac{(2 x-5)(x+2)}{(x+9)(x-3)} \div \frac{(x+2)(3 x+5)}{(x+9)(x-3)}$

A) $-\frac{2 x-5}{3 x+5}$

B) $\frac{x-9}{x+2}$

C) $\frac{2 x-5}{3 x+5}$

D) $\frac{2}{3}$

Question 47

Perform the indicated operation and express in lowest terms.

- $\frac{4 x^{2}-19 x y-5 y^{2}}{y^{2}+4 x y-5 x^{2}} \cdot \frac{y^{2}+3 x y-4 x^{2}}{8 x^{2}+6 x y+y^{2}} \div \frac{4 x^{2}-19 x y-5 y^{2}}{10 x^{2}+3 x y-y^{2}}$

A) $\frac{x-5 y}{y+5 x}$

B) $\frac{5 x-y}{5 x+y}$

C) $\frac{(y+4 x)^{2}}{2 x-y}$

D) 1

Question 48

Perform the indicated operation and express in lowest terms.

- $\frac{16 s^{2}+8 s t+t^{2}}{2 s^{2}-9 s t-5 t^{2}} \cdot \frac{2 s^{2}-11 s t+5 t^{2}}{t^{2}+3 s t-4 s^{2}} \div \frac{8 s^{2}-2 s t-t^{2}}{2 s^{2}+3 s t+t^{2}}$

A) $\frac{t+s}{t-s}$

B) $\frac{(\mathrm{t}+4 \mathrm{~s})}{(\mathrm{t}+\mathrm{s})(\mathrm{t}-\mathrm{s})}$

C) 1

D) $\frac{(t+4 x)^{2}(2 x-t)^{2}}{(4 s+t)^{2}\left(t^{2}-s^{2}\right)}$

Question 49

Perform the indicated operation and express in lowest terms.

- $\frac{2 k^{2}+15 k p+18 p^{2}}{9 k^{2}-18 k p+8 p^{2}} \div \frac{6 k^{2}+17 k p+12 p^{2}}{9 k^{2}-16 p^{2}}$

A) $\frac{k+p}{3 k+2 p}$

B) $\frac{k+6 p}{3 k-2 p}$

C) $\frac{k+7 p}{2 k-3 p}$

D) -1

Question 50

Perform the indicated operation and express in lowest terms.

- $\frac{3 x^{2}(x-2 y)-22 x(x-2 y)+7(x-2 y)}{3 x^{2}(2 y-x)-20 x(2 y-x)-7(2 y-x)} \div \frac{4 x-1}{3 x+1}$

A) $\frac{3 x+1}{x-7}$

B) $-\frac{3 x+1}{4 x-5}$

C) 1

D) $-\frac{3 x-1}{4 x-1}$

Question 51

Perform the indicated operation and express in lowest terms.

- $\frac{3}{15 x}+\frac{5}{15 x}$

A) $\frac{15 x}{8}$

B) $\frac{8}{30 x}$

C) $\frac{8}{15 x}$

D) 1

Question 52

Perform the indicated operation and express in lowest terms.

- $\frac{16}{19 x}-\frac{8}{19 x}$

A) $\frac{19 x}{8}$

B) $\frac{8}{38 x}$

C) $\frac{8}{19 x}$

D) 8

Question 53

Perform the indicated operation and express in lowest terms.

- $\frac{13}{7 x^{2}}-\frac{11}{7 x^{2}}$

A) $\frac{2}{14 x^{4}}$

B) $\frac{7}{2 x^{2}}$

C) 2

D) $\frac{2}{7 x^{2}}$

Question 54

Perform the indicated operation and express in lowest terms.

- $\frac{12}{q-9}-\frac{3}{q-9}$

A) $\frac{12(q-9)}{3(q-9)}$

B) $\frac{15}{q-9}$

C) $\frac{9}{\mathrm{q}}$

D) $\frac{9}{q-9}$

Question 55

Perform the indicated operation and express in lowest terms.

- $\frac{m^{2}-7 m}{m-4}+\frac{12}{m-4}$

A) $m+3$

B) $m-3$

C) $\frac{m^{2}-7 m+12}{m-4}$

D) $m-4$

Question 56

Perform the indicated operation and express in lowest terms.

- $\frac{2 x+7}{x^{2}+4 x+3}-\frac{x+4}{x^{2}+4 x+3}$

A) $\frac{1}{x+1}$

B) $\frac{x+11}{x^{2}+4 x+3}$

C) $x+3$

D) $\frac{8}{x^{2}+4 x+3}$

Question 57

Perform the indicated operation and express in lowest terms.

- $\frac{3 x+16}{x^{2}+3 x-10}-\frac{x+6}{x^{2}+3 x-10}$

A) $\frac{1}{x-1}$

B) $\frac{2}{x-2}$

C) $\frac{2 x+22}{x^{2}+3 x-10}$

D) $2 x+10$

Question 58

Perform the indicated operation and express in lowest terms.

- $\frac{125 x^{3}+125 x^{2} y}{25 x^{2}+50 x y+25 y^{2}}-\frac{125 x y^{2}+125 y^{3}}{25 x^{2}+50 x y+25 y^{2}}$

A) $\frac{x-y}{25 x^{2}+25 x y+25 y^{2}}$

B) $5 y-5 x$

C) $\frac{5 x^{2}-5 y^{2}}{5 x+5 y}$

D) $5 x-5 y$

Question 59

Assume that the expressions given are denominators of fractions. Find the least common denominator.

- $t, t+7$

A) $\mathrm{t}(\mathrm{t}+7)$
B) -7
C) $t+7$
D) 7

Question 60

Assume that the expressions given are denominators of fractions. Find the least common denominator.

- $7 a+21, a^{2}+3 a$

A) $7 \mathrm{a}^{2}+21$
B) $7 a+3$
C) $7 a^{2}+3$
D) $7 \mathrm{a}(\mathrm{a}+3)$

Question 61

Assume that the expressions given are denominators of fractions. Find the least common denominator.

- $15 x y, 6 x^{2}$

A) $30 x^{2} y$
B) $30 x y^{2}$
C) $30 x y^{3}$
D) $30 x^{3} y$

Question 62

Assume that the expressions given are denominators of fractions. Find the least common denominator.

- $r^{2}+4 r+3, r^{2}+r$

A) $r(r+3)(r+1)$
B) $r(r+3)$
C) $r(r+1)$
D) $r(r+1)^{2}$

Question 63

Assume that the expressions given are denominators of fractions. Find the least common denominator.

- $m^{2}-5 m, m^{2}-11 m+30$

A) $(m+1)^{2}$
B) $m(m+1)(m-6)$
C) $m(m-5)(m-6)$
D) $\mathrm{m}(\mathrm{m}+1)^{2}$

Question 64

Assume that the expressions given are denominators of fractions. Find the least common denominator.

- $x^{2}-5 x+6, x^{2}-8 x+12$

A) $(x-2)(x-6)$
B) $(x-3)(x-2)(x-6)$
C) $(x-3)(x-2)$
D) $(x+3)(x+2)(x-6)$

Question 65

Assume that the expressions given are denominators of fractions. Find the least common denominator.

- $x^{2}+4 x-12,5 x+30$

A) $5(x+2)(x+6)$
B) $5(x-2)(x+6)$
C) $5(x+2)(x-6)$
D) $5(x-2)(x-6)$

Question 66

Assume that the expressions given are denominators of fractions. Find the least common denominator.

- $7 y+14, y^{2}-4, y$

A) $14 y(y+2)^{2}(y-2)$
B) $14 y\left(y^{2}+2\right)\left(y^{2}-2\right)$
C) $7 y(y+2)(y-2)$
D) $y(y+2)(y-2)$

Question 67

Assume that the expressions given are denominators of fractions. Find the least common denominator.

- $a+b, a-b, a^{2}-b^{2}$

A) $b(a+b)$
B) $(a+b)^{2}(a-b)^{2}$
C) $a(a-b)$
D) $(a+b)(a-b)$

Question 68

Assume that the expressions given are denominators of fractions. Find the least common denominator.

- $15 \mathrm{a}^{3} \mathrm{~b}^{4}, 20 \mathrm{a}^{2} \mathrm{~b}^{5}$

A) $60 a^{2} b^{4}$
B) $300 a^{3} b^{5}$
C) $300 a^{5} b^{9}$
D) $60 \mathrm{a}^{3} \mathrm{~b}^{5}$

Question 69

Add or subtract as indicated. Write the answer in lowest terms.

- $\frac{2}{r}+\frac{3}{r-8}$

A) $\frac{16 r-5}{r(8-r)}$

B) $\frac{5 r-16}{r(8-r)}$

C) $\frac{5 r-16}{r(r-8)}$

D) $\frac{16 r-5}{r(r-8)}$

Question 70

Add or subtract as indicated. Write the answer in lowest terms.

- $\frac{2}{r}+\frac{3}{r+6}$

A) $\frac{-12 r-5}{r(r+6)}$

B) $\frac{-12 r-5}{r(-6-r)}$

C) $\frac{5 r+12}{r(r+6)}$

D) $\frac{5 r+12}{r(-6-r)}$

Question 71

Add or subtract as indicated. Write the answer in lowest terms.

- $\frac{4}{y^{2}-3 y+2}+\frac{7}{y^{2}-1}$

A) $\frac{11 y-10}{(y-1)(y+1)(y-2)}$

B) $\frac{56 y-10}{(y-1)(y+1)(y-2)}$

C) $\frac{11 \mathrm{y}-10}{(\mathrm{y}-1)(\mathrm{y}-2)}$

D) $\frac{10 y-11}{(y-1)(y+1)(y-2)}$

Question 72

Add or subtract as indicated. Write the answer in lowest terms.

- $\frac{x}{x^{2}-16}-\frac{7}{x^{2}+5 x+4}$

A) $\frac{x^{2}+6 x+28}{(x-4)(x+4)(x+1)}$

B) $\frac{x^{2}-6 x+28}{(x-4)(x+4)(x+1)}$

C) $\frac{x^{2}-6 x+28}{(x-4)(x+4)}$

D) $\frac{x^{2}-6}{(x-4)(x+4)(x+1)}$

Question 73

Add or subtract as indicated. Write the answer in lowest terms.

- $\frac{6}{x}+\frac{7}{5 x}$

A) $\frac{37}{5 x}$

B) $\frac{37 x}{5}$

C) $\frac{13}{x^{2}}$

D) $-\frac{37}{x}$

Question 74

Add or subtract as indicated. Write the answer in lowest terms.

- $\frac{1}{12 x^{3} y^{2}}-\frac{11}{3 x y}$

A) $\frac{1-44 x^{2} y}{12 x^{3} y^{2}}$

B) $\frac{10-44 x^{3} y}{12 x^{4} y^{3}}$

C) $\frac{1-44 x y}{12 x^{3} y^{2}}$

D) $\frac{8-44 x^{4}}{12 x^{3} y}$

Question 75

Add or subtract as indicated. Write the answer in lowest terms.

- $\frac{2 a b}{a^{2}-b^{2}}-\frac{b}{a-b}+4$

A) $\frac{2 a b-b+4}{a+b+1}$

B) $\frac{(a-b)(5 a+5 b)}{a^{2}-b^{2}}$

C) $\frac{4 a+5 b}{a+b}$

D) $\frac{4 a+5 b}{a^{2}-b^{2}}$

Question 76

Add or subtract as indicated. Write the answer in lowest terms.

- $\frac{2}{x-5}-\frac{8}{5-x}$

A) $\frac{10}{x-5}$

B) $\frac{12}{x-5}$

C) -1

D) $\frac{-6}{x+5}$

Question 77

Add or subtract as indicated. Write the answer in lowest terms.

- $\frac{5}{x+2}+\frac{2}{x^{2}-2 x+4}-\frac{60}{x^{3}+8}$

A) $\frac{5 x-18}{x^{2}-2 x+4}$

B) $-\frac{1}{x^{2}-4}$

C) $\frac{7 x-20}{x+2}$

D) $\frac{5 x-18}{x^{3}-8}$

Question 78

Find the requested expression for the function.

-If $x$ represents the size of the order to replenish an inventory of computers, then the annual inventory cost is given by the function $c(x)=\frac{2,000,000}{x}+\frac{73}{10}$ . Simplify the expression for $c(x)$ by performing the indicated addition.

A) $c(x)=\frac{20,000,000+73 x}{5 x}$

B) $c(x)=\frac{2,000,073}{10 x}$

C) $c(x)=\frac{2,000,000+73 x}{x}$

D) $c(x)=\frac{20,000,000+73 x}{10 x}$

Question 79

Find the requested expression for the function.

-A cost-benefit model expresses the cost of an undertaking in terms of the benefits received. One cost-benefit model gives the cost in thousands of dollars to clean up $x$ percent of an oil spill as $c(x)=\frac{7.5 x}{50-x}$ . Another model produces the relationship $c(x)=\frac{7.2 x}{52-x}$ . Find the cost function found by averaging the two models. Simplify the expression for this function by performing the indicated operations.

A) $c(x)=\frac{750 x-14.7 x^{2}}{2(50-x)(52-x)}$

B) $c(x)=\frac{750 x-14.7 x^{2}}{(50-x)(52-x)}$

C) $c(x)=\frac{735.6 x-15.7 x^{2}}{(50-x)(52-x)}$

D) $c(x)=\frac{1500 x-29.4 x^{2}}{(50-x)(52-x)}$

Question 80

Use the example to give a step-by-step explanation of the method to add or subtract two fractions with a common denominator.
$\frac{15}{p+3}+\frac{5 p}{p+3}$