Multiply.
-$\frac { x ^ { 2 } + 12 x + 32 } { x ^ { 2 } + 13 x + 36 } \cdot \frac { x ^ { 2 } + 9 x } { x ^ { 2 } + 6 x - 16 }$
A) $\frac { x } { x ^ { 2 } + 13 x + 36 }$
B) $\frac { 1 } { x - 2 }$
C) $\frac { x } { x - 2 }$
D) $\frac { x ( x + 9 ) } { x - 2 }$

Question

Quizplus · Accepted Answer

First, factor each polynomial where possible. The given expression is:$\frac { x ^ { 2 } + 12 x + 32 } { x ^ { 2 } + 13 x + 36 } \cdot \frac { x ^ { 2 } + 9 x } { x ^ { 2 } + 6 x - 16 }$Factoring each part:$\frac { (x + 4)(x + 8) } { (x + 4)(x + 9) } \cdot \frac { x(x + 9) } { (x + 8)(x - 2) }$Simplifying by canceling out common factors:$\frac { x } { x - 2 }$Thus, the correct answer is C, $\frac { x } { x - 2 }$.

Multiply - x2+12x+32x2+13x+36⋅x2+9xx2+6x−16\frac { x ^ { 2 } + 12 x + 32 } { x ^ { 2 } + 13 x + 36 } \cdot \frac { x ^ { 2 } + 9 x } { x ^ { 2 } + 6 x - 16 }x2+13x+36x2+12x+32​⋅x2+6x−16x2+9x​

Multiply
- $\frac { x ^ { 2 } + 12 x + 32 } { x ^ { 2 } + 13 x + 36 } \cdot \frac { x ^ { 2 } + 9 x } { x ^ { 2 } + 6 x - 16 }$