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.

$$b=\frac{ac}{a+c}\text{, }b\neq 0$$