Question

In the following exercises, solve

$\frac{a}{9}+\frac{a+3}{3a}=\frac{1}{a}$

Short answer

The solution is$a=0,-3.$

Step-by-step solution

Step 1. Given Information

The given rational expression is$\frac{a}{9}+\frac{a+3}{3a}=\frac{1}{a}$

Step 2. Remove the fraction

The least common denominator is $9a$

Multiply the equation by LCD

$$\begin{gathered} 9a\{\frac{a}{9}+\frac{a+3}{3a}\}=\frac{1}{a}\times 9a \\ a\times a+3(a+3)=9 \\ {a}^2+3a+9=9 \\ {a}^2+3a=0 \\ a(a+3)=0 \end{gathered}$$

Step 3. Solution of the equation

Using the Zero Product Property,

The solution of the equation is

$$\begin{gathered} a=0;a+3=0 \\ a=0;a=-3 \end{gathered}$$