Perform the indicated operation. Simplify if possible.
-$\frac { 7 } { x } \cdot \left( \frac { 2 } { x + 2 } - \frac { 2 } { x - 2 } \right)$
A) $\frac { 28 } { x ( x + 2 ) ( x - 2 ) }$
B) $- \frac { 28 } { x ( x + 2 ) ( x - 2 ) }$
C) $ - \frac { 56 } { x ( x + 2 ) ( x - 2 ) }$
D) $\frac { 56 } { x ( x + 2 ) ( x - 2 ) }$

Question

Quizplus · Accepted Answer

First, find a common denominator for the terms inside the parentheses: $\frac{2}{x+2} - \frac{2}{x-2} = \frac{2(x-2) - 2(x+2)}{(x+2)(x-2)} = \frac{-8}{(x+2)(x-2)}$. Then multiply by $\frac{7}{x}$: $\frac{7}{x} \cdot \frac{-8}{(x+2)(x-2)} = -\frac{56}{x(x+2)(x-2)}$.

Perform the Indicated Operation 7x⋅(2x+2−2x−2)\frac { 7 } { x } \cdot \left( \frac { 2 } { x + 2 } - \frac { 2 } { x - 2 } \right)x7​⋅(x+22​−x−22​)

Perform the Indicated Operation $\frac { 7 } { x } \cdot \left( \frac { 2 } { x + 2 } - \frac { 2 } { x - 2 } \right)$