Solve by Factoring 1/a-5/(3a)=1/3

$\frac{1}{a} - \frac{5}{3 a} = \frac{1}{3}$

Step 1

Subtract $\frac{1}{3}$ from both sides of the equation.

$\frac{1}{a} - \frac{5}{3 a} - \frac{1}{3} = 0$

Step 2

Simplify $\frac{1}{a} - \frac{5}{3 a} - \frac{1}{3}$ .

To write $\frac{1}{a}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{a} \cdot \frac{3}{3} - \frac{5}{3 a} - \frac{1}{3} = 0$

Write each expression with a common denominator of $a \cdot 3$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{a}$ by $\frac{3}{3}$ .

$\frac{3}{a \cdot 3} - \frac{5}{3 a} - \frac{1}{3} = 0$

Move $3$ to the left of $a$ .

$\frac{3}{3 a} - \frac{5}{3 a} - \frac{1}{3} = 0$

Combine the numerators over the common denominator.

$\frac{3 - 5}{3 a} - \frac{1}{3} = 0$

Subtract $5$ from $3$ .

$\frac{- 2}{3 a} - \frac{1}{3} = 0$

Move the negative in front of the fraction.

$- \frac{2}{3 a} - \frac{1}{3} = 0$

Step 3

Factor $- 1$ out of $- \frac{2}{3 a} - \frac{1}{3}$ .

Factor $- 1$ out of $- \frac{2}{3 a}$ .

$- (\frac{2}{3 a}) - \frac{1}{3} = 0$

Factor $- 1$ out of $- \frac{1}{3}$ .

$- (\frac{2}{3 a}) - (\frac{1}{3}) = 0$

Factor $- 1$ out of $- (\frac{2}{3 a}) - (\frac{1}{3})$ .

$- (\frac{2}{3 a} + \frac{1}{3}) = 0$

Step 4

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{a}{a}$ .

$- (\frac{2}{3 a} + \frac{1}{3} \cdot \frac{a}{a}) = 0$

Step 5

Multiply $\frac{1}{3}$ by $\frac{a}{a}$ .

$- (\frac{2}{3 a} + \frac{a}{3 a}) = 0$

Step 6

Combine the numerators over the common denominator.

$- \frac{2 + a}{3 a} = 0$

Step 7

Set the numerator equal to zero.

$2 + a = 0$

Step 8

Subtract $2$ from both sides of the equation.

$a = - 2$