Solve 1/3-1/a=1/b

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

Solve for a

$$a=\frac{3b}{b-3}$$

$$b\neq 0\text{ and }b\neq 3$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3ab, the least common multiple of 3,a,b.

$$3ab\times \frac{1}{3}-3b=3a$$

Multiply 3 and \frac{1}{3} to get 1.

$$ab-3b=3a$$

Subtract 3a from both sides.

$$ab-3b-3a=0$$

Add 3b to both sides. Anything plus zero gives itself.

$$ab-3a=3b$$

Combine all terms containing a.

$$\left(b-3\right)a=3b$$

Divide both sides by -3+b.

$$\frac{\left(b-3\right)a}{b-3}=\frac{3b}{b-3}$$

Dividing by -3+b undoes the multiplication by -3+b.

$$a=\frac{3b}{b-3}$$

Variable a cannot be equal to 0.

$$a=\frac{3b}{b-3}\text{, }a\neq 0$$

Solve for b

$$b=\frac{3a}{a-3}$$

$$a\neq 0\text{ and }a\neq 3$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3ab, the least common multiple of 3,a,b.

$$3ab\times \frac{1}{3}-3b=3a$$

Multiply 3 and \frac{1}{3} to get 1.

$$ab-3b=3a$$

Combine all terms containing b.

$$\left(a-3\right)b=3a$$

Divide both sides by a-3.

$$\frac{\left(a-3\right)b}{a-3}=\frac{3a}{a-3}$$

Dividing by a-3 undoes the multiplication by a-3.

$$b=\frac{3a}{a-3}$$

Variable b cannot be equal to 0.

$$b=\frac{3a}{a-3}\text{, }b\neq 0$$