# Question #53ca1

Aug 8, 2017

$\frac{1}{p} - \frac{1}{q} = \frac{1}{3}$

#### Explanation:

We can arrive at this answer rather quickly if we think outside the box. Instead to solving for p and q, we can rearrange equations to suit our needs.

Our First step would be to cross multiply

$\frac{1}{p} - \frac{1}{q}$

which will give us

$\frac{q - p}{p q}$

Seem familiar? We already know what $p q$ is, so we just need to figure out what $q - p$ equals to. By rearranging the first equation(basically flipping it), we get

$p - q = - \frac{1}{12}$

Substituting these values into the formula will give us a value which is

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