Solve 1/A=1/B-1/C

$$\frac { 1 } { A } = \frac { 1 } { B } - \frac { 1 } { C }$$

Solve for A

$$A=-\frac{BC}{B-C}$$

$$C\neq 0\text{ and }B\neq 0\text{ and }B\neq C$$

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 ABC, the least common multiple of A,B,C.

$$BC=AC-AB$$

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

$$AC-AB=BC$$

Reorder the terms.

$$-AB+AC=BC$$

Combine all terms containing A.

$$\left(-B+C\right)A=BC$$

The equation is in standard form.

$$\left(C-B\right)A=BC$$

Divide both sides by C-B.

$$\frac{\left(C-B\right)A}{C-B}=\frac{BC}{C-B}$$

Dividing by C-B undoes the multiplication by C-B.

$$A=\frac{BC}{C-B}$$

Variable A cannot be equal to 0.

$$A=\frac{BC}{C-B}\text{, }A\neq 0$$

Solve for B

$$B=\frac{AC}{A+C}$$

$$C\neq 0\text{ and }A\neq 0\text{ and }A\neq -C$$

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 ABC, the least common multiple of A,B,C.

$$BC=AC-AB$$

Add AB to both sides.

$$BC+AB=AC$$

Combine all terms containing B.

$$\left(C+A\right)B=AC$$

The equation is in standard form.

$$\left(A+C\right)B=AC$$

Divide both sides by C+A.

$$\frac{\left(A+C\right)B}{A+C}=\frac{AC}{A+C}$$

Dividing by C+A undoes the multiplication by C+A.

$$B=\frac{AC}{A+C}$$

Variable B cannot be equal to 0.

$$B=\frac{AC}{A+C}\text{, }B\neq 0$$