Question

Solve:$\frac{2}{x}+\frac{1}{3}=\frac{1}{y}$for$y.$

Short answer

The solution is$y=\frac{3x}{x+6}$.

Step-by-step solution

Step 1. Given  

The given equation is: $\frac{2}{x}+\frac{1}{3}=\frac{1}{y}$.

Step 2. To find  

We have to solve the equation for y.

Step 3. Calculation 

We will solve this problem using LCD.

$$\begin{gathered} \frac{2}{x}+\frac{1}{3}=\frac{1}{y} \\ \frac{2}{x}\left(3xy\right)+\frac{1}{3}\left(3xy\right)=\frac{1}{y}\left(3xy\right) \\ 2\left(3y\right)+1\left(xy\right)=1\left(3x\right) \\ 6y+xy=3x \\ y(6+x)=3x \\ y=\frac{3x}{6+x} \\ y=\frac{3x}{x+6} \end{gathered}$$