Perform the operation indicated.
-$$\frac { x ^ { 2 } + 7 x + 12 } { x ^ { 2 } + 10 x + 24 } \cdot \frac { x ^ { 2 } + 6 x } { x ^ { 2 } + 8 x + 15 }$$
A) $\frac { x } { x ^ { 2 } + 10 x + 24 }$
B) $\frac { x ^ { 2 } + 6 x } { x + 5 }$
C) $\frac { 1 } { x + 5 }$
D) $\frac { x } { x + 5 }$

Question

Quizplus · Accepted Answer

First, factorize all the quadratic expressions: $\frac{(x+3)(x+4)}{(x+4)(x+6)} \cdot \frac{x(x+6)}{(x+3)(x+5)}$. Canceling common factors, we get $\frac{x}{x+5}$.

Perform the Operation Indicated x2+7x+12x2+10x+24⋅x2+6xx2+8x+15\frac { x ^ { 2 } + 7 x + 12 } { x ^ { 2 } + 10 x + 24 } \cdot \frac { x ^ { 2 } + 6 x } { x ^ { 2 } + 8 x + 15 }x2+10x+24x2+7x+12​⋅x2+8x+15x2+6x​

Perform the Operation Indicated $\frac { x ^ { 2 } + 7 x + 12 } { x ^ { 2 } + 10 x + 24 } \cdot \frac { x ^ { 2 } + 6 x } { x ^ { 2 } + 8 x + 15 }$