# How do you solve 4/v + 1/5 = 1 and find any extraneous solutions?

Jul 10, 2017

$v = 5$

#### Explanation:

$\text{subtract " 1/5" from both sides}$

$\frac{4}{v} \cancel{+ \frac{1}{5}} \cancel{- \frac{1}{5}} = 1 - \frac{1}{5}$

$\Rightarrow \frac{4}{v} = \frac{4}{5}$

$\text{since the fractions are equal and have the same numerator}$

$\Rightarrow v = 5$

$\textcolor{b l u e}{\text{As a check}}$

$\text{left side "=4/5+1/5=5/5=1=" right side}$

$\Rightarrow v = 5 \text{ is the solution}$