Multiply the rational expressions. $$\frac { 2 x ^ { 2 } - 4 x - 6 } { x + 2 } \cdot \frac { x ^ { 2 } - 4 } { 2 x ^ { 2 } + 2 x }$$
A) $\frac { ( x - 3 ) ( x - 2 ) ^ { 2 } } { x ( x + 2 ) }$
B) $\frac { ( x - 3 ) ( x - 2 ) } { x }$
C) $\frac { ( 2 x + 2 ) ( x - 3 ) } { x + 2 }$
D) $\frac { ( x - 3 ) ( x + 2 ) } { 2 x ^ { 2 } + 2 x }$

Question

Quizplus · Accepted Answer

First, factorize each polynomial: $2x^2 - 4x - 6 = 2(x^2 - 2x - 3) = 2(x - 3)(x + 1)$, $x^2 - 4 = (x - 2)(x + 2)$, and $2x^2 + 2x = 2x(x + 1)$. Then, simplify the expression: $\frac{2(x - 3)(x + 1)}{x + 2} \cdot \frac{(x - 2)(x + 2)}{2x(x + 1)}$. Cancel common factors to get $\frac{(x - 3)(x - 2)}{x}$.

Multiply the Rational Expressions 2x2−4x−6x+2⋅x2−42x2+2x\frac { 2 x ^ { 2 } - 4 x - 6 } { x + 2 } \cdot \frac { x ^ { 2 } - 4 } { 2 x ^ { 2 } + 2 x }x+22x2−4x−6​⋅2x2+2xx2−4​

Multiply the Rational Expressions $\frac { 2 x ^ { 2 } - 4 x - 6 } { x + 2 } \cdot \frac { x ^ { 2 } - 4 } { 2 x ^ { 2 } + 2 x }$