Solve 1/f=1/a+1/b

$$\frac { 1 } { f } = \frac { 1 } { a } + \frac { 1 } { b }$$

Solve for a

$$a=-\frac{bf}{f-b}$$

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

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 abf, the least common multiple of f,a,b.

$$ab=bf+af$$

Subtract af from both sides.

$$ab-af=bf$$

Combine all terms containing a.

$$\left(b-f\right)a=bf$$

Divide both sides by b-f.

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

Dividing by b-f undoes the multiplication by b-f.

$$a=\frac{bf}{b-f}$$

Variable a cannot be equal to 0.

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

Solve for b

$$b=-\frac{af}{f-a}$$

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

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 abf, the least common multiple of f,a,b.

$$ab=bf+af$$

Subtract bf from both sides.

$$ab-bf=af$$

Combine all terms containing b.

$$\left(a-f\right)b=af$$

Divide both sides by a-f.

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

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

$$b=\frac{af}{a-f}$$

Variable b cannot be equal to 0.

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