Multiply and, if possible, simplify.
-$$\frac { k ^ { 2 } + 9 k + 20 } { k ^ { 2 } + 12 k + 32 } \cdot \frac { k ^ { 2 } + 8 k } { k ^ { 2 } + 10 k + 25 }$$
A) $\frac { k } { k ^ { 2 } + 12 k + 32 }$
B) $\frac { \mathrm { k } } { \mathrm { k } + 5 }$
C) $\frac { k ^ { 2 } + 8 k } { k + 5 }$
D) $\frac { 1 } { \mathrm { k } + 5 }$

Question

Quizplus · Accepted Answer

First, factor each polynomial:- The numerator of the first fraction, $k^2 + 9k + 20$, factors to $(k+4)(k+5)$.- The denominator of the first fraction, $k^2 + 12k + 32$, factors to $(k+4)(k+8)$.- The numerator of the second fraction, $k^2 + 8k$, factors to $k(k+8)$.- The denominator of the second fraction, $k^2 + 10k + 25$, factors to $(k+5)^2$.After factoring, the expression becomes:$$\frac{(k+4)(k+5)}{(k+4)(k+8)} \cdot \frac{k(k+8)}{(k+5)^2}$$Cancel out the common terms:- $k+4$ in the numerator and denominator of the first fraction.- $k+8$ in the numerator of the second fraction and the denominator of the first fraction.This leaves us with:$$\frac{k(k+5)}{(k+5)^2}$$Further simplification by canceling out $k+5$ gives:$$\frac{k}{k+5}$$Therefore, the correct answer is B) $\frac{k}{k+5}$.

Multiply And, If Possible, Simplify k2+9k+20k2+12k+32⋅k2+8kk2+10k+25\frac { k ^ { 2 } + 9 k + 20 } { k ^ { 2 } + 12 k + 32 } \cdot \frac { k ^ { 2 } + 8 k } { k ^ { 2 } + 10 k + 25 }k2+12k+32k2+9k+20​⋅k2+10k+25k2+8k​

Multiply And, If Possible, Simplify $\frac { k ^ { 2 } + 9 k + 20 } { k ^ { 2 } + 12 k + 32 } \cdot \frac { k ^ { 2 } + 8 k } { k ^ { 2 } + 10 k + 25 }$