Question

multiply: $\frac{x^2 - 4}{x^2 - 1} cdot \frac{x + 1}{x^2 + 2x}$
a. $\frac{x - 2}{x(x - 1)}$
b. $\frac{x - 2}{x - 1}$
c. $\frac{x - 2}{x + 1}$
d. $x - 2$

Explanation:

Step1: Factor all expressions

$x^2-4=(x+2)(x-2)$, $x^2-1=(x+1)(x-1)$, $x^2+2x=x(x+2)$
Original expression becomes: $\frac{(x+2)(x-2)}{(x+1)(x-1)} \cdot \frac{x+1}{x(x+2)}$

Step2: Cancel common factors

Cancel $(x+2)$ and $(x+1)$: $\frac{x-2}{(x-1)} \cdot \frac{1}{x}$

Step3: Simplify the product

$\frac{x-2}{x(x-1)}$

Answer:

A. $\frac{x-2}{x(x-1)}$