Multiply the rational expressions.
-$$\frac { 2 x ^ { 2 } - 2 x - 12 } { x + 5 } \cdot \frac { x ^ { 2 } - 25 } { 2 x ^ { 2 } + 4 x }$$
A) $\frac { ( x - 3 ) ( x + 5 ) } { 2 x ^ { 2 } + 5 x }$
B) $\frac { ( x - 3 ) ( x - 5 ) } { x }$
C) $\frac { ( 2 x + 4 ) ( x - 3 ) } { x + 4 }$
D) $\frac { ( x - 3 ) ( x - 5 ) ^ { 2 } } { x ( x + 5 ) }$

Question

Quizplus · Accepted Answer

First, factorize the numerators and denominators where possible. The expression simplifies to $\frac{(2x^2-2x-12)}{(x+5)} \cdot \frac{(x+5)(x-5)}{(2x)(x+2)}$, which further simplifies to $\frac{(2(x^2-x-6))(x-5)}{2x(x+2)}$. Factoring $x^2-x-6$ gives $(x-3)(x+2)$, leading to $\frac{(2(x-3)(x+2))(x-5)}{2x(x+2)}$. Canceling out the common terms, we get $\frac{(x-3)(x-5)}{x}$.

Multiply the Rational Expressions 2x2−2x−12x+5⋅x2−252x2+4x\frac { 2 x ^ { 2 } - 2 x - 12 } { x + 5 } \cdot \frac { x ^ { 2 } - 25 } { 2 x ^ { 2 } + 4 x }x+52x2−2x−12​⋅2x2+4xx2−25​

Multiply the Rational Expressions $\frac { 2 x ^ { 2 } - 2 x - 12 } { x + 5 } \cdot \frac { x ^ { 2 } - 25 } { 2 x ^ { 2 } + 4 x }$