# How do you solve 3/x - 2/(5x) = 13?

Apr 17, 2018

#### Answer:

$x = \frac{1}{5}$

#### Explanation:

Fairfax? Like in Virginia?

$\frac{3}{x} - \frac{2}{5 x} = 13$

The first thing to do is remove the fear factor $-$ having variables in denominators of quotients. This can be easily remedied by multiplying both sides of this equation by $x$.

$3 - \frac{2}{5} = 13 x$

There now. Not as scary, but we still need to know how to deal with fractions. Watch closely:

$3 - \frac{2}{5} = 3 \cdot \frac{5}{5} - \frac{2}{5} = \frac{15}{5} - \frac{2}{5} = \frac{13}{5} = 13 x$

Since $\frac{13}{5} = 13 x$, we can divide both sides of this equation by 13 to get

$\frac{1}{5} = x$.