# How do you evaluate \frac{x-9}{4}\div \frac{x}{8}?

Aug 9, 2017

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$\frac{\frac{x - 9}{4}}{\frac{x}{8}}$

Now, use this rule for dividing fractions to evaluate the expression:

$\frac{\frac{\textcolor{red}{a}}{\textcolor{b l u e}{b}}}{\frac{\textcolor{g r e e n}{c}}{\textcolor{p u r p \le}{d}}} = \frac{\textcolor{red}{a} \times \textcolor{p u r p \le}{d}}{\textcolor{b l u e}{b} \times \textcolor{g r e e n}{c}}$

$\frac{\frac{\textcolor{red}{\left(x - 9\right)}}{\textcolor{b l u e}{4}}}{\frac{\textcolor{g r e e n}{x}}{\textcolor{p u r p \le}{8}}} \implies \frac{\textcolor{red}{\left(x - 9\right)} \times \textcolor{p u r p \le}{8}}{\textcolor{b l u e}{4} \times \textcolor{g r e e n}{x}} \implies \frac{\textcolor{red}{\left(x - 9\right)} \times \cancel{\textcolor{p u r p \le}{8}} \textcolor{p u r p \le}{2}}{\cancel{\textcolor{b l u e}{4}} \times \textcolor{g r e e n}{x}} \implies$

$\frac{\textcolor{p u r p \le}{2} \textcolor{red}{\left(x - 9\right)}}{\textcolor{g r e e n}{x}} \implies \frac{\left(\textcolor{p u r p \le}{2} \times \textcolor{red}{x}\right) - \left(\textcolor{p u r p \le}{2} \times \textcolor{red}{9}\right)}{\textcolor{g r e e n}{x}} \implies$

$\frac{2 x - 18}{x}$