Question

In the following exercises, solve.

$\frac{4}{5}+\frac{1}{4}=\frac{2}{v}$

Short answer

The solution of the equation$\frac{4}{5}+\frac{1}{4}=\frac{2}{v}$is

$v=\frac{40}{21}$

Step-by-step solution

Step 1. Given information

The given equation is

$\frac{4}{5}+\frac{1}{4}=\frac{2}{v}$

Step 2. Solution of equation 

In the equation, the term $\frac{2}{v}$is undefined for$v=0$

sorole="math" localid="1647784533673" $\frac{4}{5}+\frac{1}{4}=\frac{2}{v},v\ne 0$

the least common denominator of all denominators in the equation is$20v$

multiply both sides of the equation by the least common denominator$20v$

$$\begin{gathered} 20v\left(\frac{4}{5}+\frac{1}{4}\right)=20v\left(\frac{2}{v}\right) \\ 20v\left(\frac{4}{5}\right)+20v\left(\frac{1}{4}\right)=20v\left(\frac{2}{v}\right) \\ 16v+5v=40 \\ 21v=40 \\ v=\frac{40}{21} \end{gathered}$$

So the solution of the equation is$v=\frac{40}{21}$

Step 3. Verification 

Substitute $v=\frac{40}{21}$in the equation

$$\begin{gathered} \frac{4}{5}+\frac{1}{4}=\frac{2}{v} \\ \frac{4}{5}+\frac{1}{4}\stackrel{?}{=}\frac{2}{\frac{40}{21}} \\ \frac{16}{20}+\frac{5}{20}\stackrel{?}{=}\frac{42}{40} \\ \frac{21}{20}=\frac{21}{20} \end{gathered}$$

The left-hand side is equal to the right-hand side so the solution is correct.