Question

question #5
simplify the rational expression $\frac{x^{2}-4}{x^{2}+2x}$
$\frac{x}{x + 2}$
$\frac{-4}{x^{2}}$
$\frac{x + 2}{x}$
$\frac{x - 2}{x}$

Explanation:

Step1: Factor numerator and denominator

The numerator $x^{2}-4$ is a difference - of - squares and can be factored as $(x + 2)(x - 2)$ using the formula $a^{2}-b^{2}=(a + b)(a - b)$ where $a=x$ and $b = 2$. The denominator $x^{2}+2x$ can be factored as $x(x + 2)$ by taking out the common factor $x$. So the expression becomes $\frac{(x + 2)(x - 2)}{x(x + 2)}$.

Step2: Cancel out common factors

Cancel out the common factor $(x + 2)$ in the numerator and the denominator. We get $\frac{x-2}{x}$, assuming $x
eq - 2$ and $x
eq0$.

Answer:

$\frac{x - 2}{x}$