# How do you evaluate \frac { 4x - 12} { 4} \div \frac { 2x - 6} { 6}?

Nov 20, 2017

See a solution process below:

#### Explanation:

First, factor the numerator of the left fraction as:

$\frac{2 \left(2 x - 6\right)}{4} \div \frac{2 x - 6}{6}$

Next, rewrite the expression as:

$\frac{\frac{2 \left(2 x - 6\right)}{4}}{\frac{2 x - 6}{6}}$

Now, use this rule for dividing fractions to complete the evaluation of the expression:

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

$\frac{\frac{\textcolor{red}{2 \left(2 x - 6\right)}}{\textcolor{b l u e}{4}}}{\frac{\textcolor{g r e e n}{2 x - 6}}{\textcolor{p u r p \le}{6}}} \implies$

$\frac{\textcolor{red}{2 \left(2 x - 6\right)} \times \textcolor{p u r p \le}{6}}{\textcolor{b l u e}{4} \times \textcolor{g r e e n}{\left(2 x - 6\right)}} \implies$

$\frac{\textcolor{red}{2 \left(2 x - 6\right)} \times \textcolor{p u r p \le}{\left(2 \times 3\right)}}{\textcolor{b l u e}{\left(2 \times 2\right) \times \textcolor{g r e e n}{\left(2 x - 6\right)}}} \implies$

$\frac{\textcolor{red}{\textcolor{b l u e}{\cancel{\textcolor{red}{2}}} \textcolor{g r e e n}{\cancel{\textcolor{red}{\left(2 x - 6\right)}}}} \times \textcolor{p u r p \le}{\left(\textcolor{b l u e}{\cancel{\textcolor{p u r p \le}{2}}} \times 3\right)}}{\textcolor{b l u e}{\left(\textcolor{red}{\cancel{\textcolor{b l u e}{2}}} \times \textcolor{p u r p \le}{\cancel{\textcolor{b l u e}{2}}}\right) \times \textcolor{g r e e n}{\textcolor{red}{\cancel{\textcolor{g r e e n}{\left(2 x - 6\right)}}}}}} \implies$

$3$