# How do you solve for p in  1/p+1/q=1/f?

Jun 2, 2016

 color(blue)(p = (fq) / (q - f )

#### Explanation:

$\frac{1}{p} + \frac{1}{q} = \frac{1}{f}$

Isolating the term containing $\textcolor{b l u e}{p}$
$\frac{1}{\textcolor{b l u e}{p}} + \frac{1}{q} = \frac{1}{f}$

$\frac{1}{\textcolor{b l u e}{p}} = \frac{1}{f} - \frac{1}{q}$

The L.C.M of the denominators of the terms on the L.H.S is color(green)(fq

$\frac{1}{p} = \frac{1 \cdot \textcolor{g r e e n}{q}}{f \cdot \textcolor{g r e e n}{q}} - \frac{1 \cdot \textcolor{g r e e n}{f}}{q \cdot \textcolor{g r e e n}{f}}$

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

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

 color(blue)(p = (fq) / (q - f )