Solve 1/x=1/a+1/b

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

Solve for a

$$a=-\frac{bx}{x-b}$$

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

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 abx, the least common multiple of x,a,b.

$$ab=bx+ax$$

Subtract ax from both sides.

$$ab-ax=bx$$

Combine all terms containing a.

$$\left(b-x\right)a=bx$$

Divide both sides by b-x.

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

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

$$a=\frac{bx}{b-x}$$

Variable a cannot be equal to 0.

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

Solve for b

$$b=-\frac{ax}{x-a}$$

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

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 abx, the least common multiple of x,a,b.

$$ab=bx+ax$$

Subtract bx from both sides.

$$ab-bx=ax$$

Combine all terms containing b.

$$\left(a-x\right)b=ax$$

Divide both sides by a-x.

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

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

$$b=\frac{ax}{a-x}$$

Variable b cannot be equal to 0.

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