How do you simplify (1-(3/x) )/ ((x/12)-(1/4))?

Oct 17, 2015

$\frac{12}{x}$

Explanation:

Your starting expression looks like this

$\frac{1 - \frac{3}{x}}{\frac{x}{12} - \frac{1}{4}}$

Start by focusing on the numerator

$1 - \frac{3}{x}$

which can be rewritten as

$1 - \frac{3}{x} = 1 \cdot \frac{x}{x} - \frac{3}{x} = \frac{x - 3}{x}$

The denominator can be written as

$\frac{x}{12} - \frac{1}{4} = \frac{x}{12} - \frac{1}{4} \cdot \frac{3}{3} = \frac{x - 3}{12}$

You know that you can write

$\textcolor{b l u e}{\frac{a}{b} = a \cdot \frac{1}{b} \text{ , } b \ne 0}$

which means that you have

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{x - 3}}}}{x} \cdot \frac{12}{\textcolor{red}{\cancel{\textcolor{b l a c k}{x - 3}}}} = \textcolor{g r e e n}{\frac{12}{x}}$