Divide.
-$$\frac { x ^ { 2 } + 10 x + 21 } { x ^ { 2 } + 12 x + 27 } \div \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 5 x - 36 }$$
A) $\frac { x - 4 } { x }$

B) $x - 4$

C) $\frac { x } { x ^ { 2 } + 12 x + 27 }$

D) $\frac { x - 4 } { x ^ { 2 } + 9 x }$

Question

Divide.
-$$\frac { x ^ { 2 } + 10 x + 21 } { x ^ { 2 } + 12 x + 27 } \div \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 5 x - 36 }$$
A) $\frac { x - 4 } { x }$

B) $x - 4$

C) $\frac { x } { x ^ { 2 } + 12 x + 27 }$

D) $\frac { x - 4 } { x ^ { 2 } + 9 x }$

Quizplus · Accepted Answer

When dividing fractions, we invert the second fraction and multiply. Thus,
$$\frac { x ^ { 2 } + 10 x + 21 } { x ^ { 2 } + 12 x + 27 } \cdot \frac { x ^ { 2 } + 5 x - 36 } { x ^ { 2 } + 7 x } $$
Factor each of the four quadratic expressions, simplify by canceling common factors, and simplify  by factoring a difference of squares in the numerator of the first fraction:
$$\frac { ( x + 3 ) ( x + 7 ) } { ( x + 3 ) ( x + 9 ) } \cdot \frac { ( x + 9 ) ( x - 4 ) } { x ( x + 7 ) } =\frac { x - 4 } { x }$$

Divide - x2+10x+21x2+12x+27÷x2+7xx2+5x−36\frac { x ^ { 2 } + 10 x + 21 } { x ^ { 2 } + 12 x + 27 } \div \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 5 x - 36 }x2+12x+27x2+10x+21​÷x2+5x−36x2+7x​

Divide
- $\frac { x ^ { 2 } + 10 x + 21 } { x ^ { 2 } + 12 x + 27 } \div \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 5 x - 36 }$