How do you solve and check for extraneous solutions in 4/v + 1/5 = 1?

Aug 14, 2015

Isolate the term containing the variable; multiply to clear the denominators and divide by the constant to get $v = 5$ then plug the solution back into the original equation to verify.

Explanation:

Given $\frac{4}{v} + \frac{1}{5} = 1$

Subtract $\frac{1}{5}$ from both sides
$\textcolor{w h i t e}{\text{XXXX}}$$\frac{4}{v} = \frac{4}{5}$
(At this point it should be obvious that $v = 5$, but continuing on...)
Multiply both sides by $5 v$
$\textcolor{w h i t e}{\text{XXXX}}$$4 \cdot 5 = 4 v$
Divide by $5$
$\textcolor{w h i t e}{\text{XXXX}}$$v = 5$

Verify that this is not an extraneous solution by substituting $\textcolor{red}{5}$ for $v$ in the original equation:

$\textcolor{w h i t e}{\text{XXXX}}$$\frac{4}{\textcolor{red}{5}} + \frac{1}{5} = 1$