Solve 1/a=1/x-1/b

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

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 a,x,b.

$$bx=ab-ax$$

Swap sides so that all variable terms are on the left hand side.

$$ab-ax=bx$$

Reorder the terms.

$$-ax+ab=bx$$

Combine all terms containing a.

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

The equation is in standard form.

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

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

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

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

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 a,x,b.

$$bx=ab-ax$$

Subtract ab from both sides.

$$bx-ab=-ax$$

Combine all terms containing b.

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

Divide both sides by x-a.

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

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

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

Variable b cannot be equal to 0.

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