Question

In the following exercises, solve.

$\frac{3}{8}+\frac{2}{y}=\frac{1}{4}$

Short answer

The solution of the equation$\frac{3}{8}+\frac{2}{y}=\frac{1}{4}$is

$y=-16$

Step-by-step solution

Step 1. Given information

The given equation is

$\frac{3}{8}+\frac{2}{y}=\frac{1}{4}$

Step 2. Solution of equation 

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

so role="math" localid="1647785717132" $\frac{3}{8}+\frac{2}{y}=\frac{1}{4},y\ne 0$

the least common denominator of all denominators in the equation is$8y$

multiply both sides of the equation by the least common denominator$8y$

$$\begin{gathered} 8y\left(\frac{3}{8}+\frac{2}{y}\right)=8y\left(\frac{1}{4}\right) \\ 8y\left(\frac{3}{8}\right)+8y\left(\frac{2}{y}\right)=8y\left(\frac{1}{4}\right) \\ 3y+16=2y \\ y=-16 \end{gathered}$$

So the solution of the equation is$y=-16$

Step 3. Verification 

Substitute $y=-16$in the equation

$$\begin{gathered} \frac{3}{8}+\frac{2}{y}=\frac{1}{4} \\ \frac{3}{8}+\frac{2}{-16}\stackrel{?}{=}\frac{1}{4} \\ \frac{6}{16}-\frac{2}{16}\stackrel{?}{=}\frac{1}{4} \\ \frac{4}{16}\stackrel{?}{=}\frac{1}{4} \\ \frac{1}{4}=\frac{1}{4} \end{gathered}$$

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