Multiply and, if possible, simplify.
-$$\frac { k ^ { 2 } + 12 k + 35 } { k ^ { 2 } + 15 k + 56 } \cdot \frac { k ^ { 2 } + 8 k } { k ^ { 2 } - 3 k - 40 }$$
A) $\frac { k } { k ^ { 2 } + 15 k + 56 }$
B) $\frac { k ^ { 2 } + 8 k } { k - 8 }$
C) $\frac { 1 } { \mathrm { k } - 8 }$
D) $\frac { k } { k - 8 }$

Question

Quizplus · Accepted Answer

First, factor all polynomials: $\frac{(k+5)(k+7)}{(k+7)(k+8)} \cdot \frac{k(k+8)}{(k-5)(k+8)}$. Cancel common factors to get $\frac{k}{k-5}$. However, there was a mistake in simplification. Correctly, after canceling, the result is $\frac{k}{k-8}$, matching option D.

Multiply And, If Possible, Simplify k2+12k+35k2+15k+56⋅k2+8kk2−3k−40\frac { k ^ { 2 } + 12 k + 35 } { k ^ { 2 } + 15 k + 56 } \cdot \frac { k ^ { 2 } + 8 k } { k ^ { 2 } - 3 k - 40 }k2+15k+56k2+12k+35​⋅k2−3k−40k2+8k​

Multiply And, If Possible, Simplify $\frac { k ^ { 2 } + 12 k + 35 } { k ^ { 2 } + 15 k + 56 } \cdot \frac { k ^ { 2 } + 8 k } { k ^ { 2 } - 3 k - 40 }$