Simplify the rational expression. (Assume the denominator is nonzero.)
-$$\frac { 4 x ^ { 2 } - 64 } { 32 - 8 x }$$
A) $- \frac { x + 4 } { 2 }$
B) $- 2 ( x + 4 )$
C) $\frac { x ^ { 2 } - 16 } { 4 - x }$

D) $\frac { x + 4 } { 2 }$

Question

Simplify the rational expression. (Assume the denominator is nonzero.)
-$$\frac { 4 x ^ { 2 } - 64 } { 32 - 8 x }$$
A) $- \frac { x + 4 } { 2 }$
B) $- 2 ( x + 4 )$
C) $\frac { x ^ { 2 } - 16 } { 4 - x }$

D) $\frac { x + 4 } { 2 }$

Quizplus · Accepted Answer

The numerator $4x^2 - 64$ can be factored as $4(x^2 - 16)$, which further simplifies to $4(x + 4)(x - 4)$ using the difference of squares formula. The denominator $32 - 8x$ can be factored out as $8(4 - x)$. Simplifying, we get $\frac{4(x + 4)(x - 4)}{8(4 - x)}$. Notice that $4 - x$ is $-1$ times $x - 4$, so when we simplify, we get $-\frac{1}{2}(x + 4)$, which matches choice A.

Simplify the Rational Expression 4x2−6432−8x\frac { 4 x ^ { 2 } - 64 } { 32 - 8 x }32−8x4x2−64​

Simplify the Rational Expression $\frac { 4 x ^ { 2 } - 64 } { 32 - 8 x }$