Solve 1/m-1/n=b

$$\frac { 1 } { m } - \frac { 1 } { n } = b$$

Solve for b

$$b=\frac{n-m}{mn}$$

$$m\neq 0\text{ and }n\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by mn, the least common multiple of m,n.

$$n-m=bmn$$

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

$$bmn=n-m$$

The equation is in standard form.

$$mnb=n-m$$

Divide both sides by mn.

$$\frac{mnb}{mn}=\frac{n-m}{mn}$$

Dividing by mn undoes the multiplication by mn.

$$b=\frac{n-m}{mn}$$

Divide n-m by mn.

$$b=\frac{1}{m}-\frac{1}{n}$$

Solve for m

$$m=\frac{n}{bn+1}$$

$$n\neq 0\text{ and }\left(b=0\text{ or }n\neq -\frac{1}{b}\right)$$

Steps for Solving Linear Equation

Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by mn, the least common multiple of m,n.

$$n-m=bmn$$

Subtract bmn from both sides.

$$n-m-bmn=0$$

Subtract n from both sides. Anything subtracted from zero gives its negation.

$$-m-bmn=-n$$

Combine all terms containing m.

$$\left(-1-bn\right)m=-n$$

The equation is in standard form.

$$\left(-bn-1\right)m=-n$$

Divide both sides by -1-nb.

$$\frac{\left(-bn-1\right)m}{-bn-1}=-\frac{n}{-bn-1}$$

Dividing by -1-nb undoes the multiplication by -1-nb.

$$m=-\frac{n}{-bn-1}$$

Divide -n by -1-nb.

$$m=\frac{n}{bn+1}$$

Variable m cannot be equal to 0.

$$m=\frac{n}{bn+1}\text{, }m\neq 0$$