# How do you solve (x+4)/(x-1) div (x^2 +x)/(x-1)?

Mar 15, 2016

$\frac{x + 4}{x \left(x + 1\right)}$

#### Explanation:

$1$. Factor the numerator of the second fraction.

$\frac{x + 4}{x - 1} \div \frac{{x}^{2} + x}{x - 1}$

$= \frac{x + 4}{x - 1} \div \frac{x \left(x + 1\right)}{x - 1}$

$2$. Take the reciprocal of the second fraction to change the operation to multiplication.

$= \frac{x + 4}{x - 1} \cdot \frac{x - 1}{x \left(x + 1\right)}$

$3$. Cancel out the factors which appear in the numerator and denominator as a pair.

$= \frac{x + 4}{\textcolor{red}{\cancel{\textcolor{b l a c k}{x - 1}}}} \cdot \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{x - 1}}}}{x \left(x + 1\right)}$

$4$. Rewrite the expression.

$= \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \frac{x + 4}{x \left(x + 1\right)} \textcolor{w h i t e}{\frac{a}{a}} |}}}$