which expression is equivalent to $\frac{2x^{2}+2x - 4}{2x^{2}-4x + 2}$?\n$\frac{x + 2}{x - 1}$\n$x +…

which expression is equivalent to $\frac{2x^{2}+2x - 4}{2x^{2}-4x + 2}$?\n$\frac{x + 2}{x - 1}$\n$x + 2$\n$-2$\n$\frac{x + 2}{x - 2}$

which expression is equivalent to $\frac{2x^{2}+2x - 4}{2x^{2}-4x + 2}$?\n$\frac{x + 2}{x - 1}$\n$x + 2$\n$-2$\n$\frac{x + 2}{x - 2}$

Answer

Answer:

A. $\frac{x + 2}{x - 1}$

Explanation:

Step1: Factor the numerator

$2x^{2}+2x - 4=2(x^{2}+x - 2)=2(x + 2)(x - 1)$

Step2: Factor the denominator

$2x^{2}-4x + 2=2(x^{2}-2x + 1)=2(x - 1)^{2}$

Step3: Simplify the fraction

$\frac{2x^{2}+2x - 4}{2x^{2}-4x + 2}=\frac{2(x + 2)(x - 1)}{2(x - 1)^{2}}=\frac{x + 2}{x - 1}$ (where $x\neq1$)