Solve n+m/mn=5

$$\frac { n + m } { m n } = 5$$

Solve for m

$$m=-\frac{n}{1-5n}$$

$$n\neq 0\text{ and }n\neq \frac{1}{5}$$

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.

$$n+m=5mn$$

Subtract 5mn from both sides.

$$n+m-5mn=0$$

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

$$m-5mn=-n$$

Combine all terms containing m.

$$\left(1-5n\right)m=-n$$

Divide both sides by 1-5n.

$$\frac{\left(1-5n\right)m}{1-5n}=-\frac{n}{1-5n}$$

Dividing by 1-5n undoes the multiplication by 1-5n.

$$m=-\frac{n}{1-5n}$$

Variable m cannot be equal to 0.

$$m=-\frac{n}{1-5n}\text{, }m\neq 0$$

Solve for n

$$n=-\frac{m}{1-5m}$$

$$m\neq 0\text{ and }m\neq \frac{1}{5}$$

Steps for Solving Linear Equation

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

$$n+m=5mn$$

Subtract 5mn from both sides.

$$n+m-5mn=0$$

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

$$n-5mn=-m$$

Combine all terms containing n.

$$\left(1-5m\right)n=-m$$

Divide both sides by 1-5m.

$$\frac{\left(1-5m\right)n}{1-5m}=-\frac{m}{1-5m}$$

Dividing by 1-5m undoes the multiplication by 1-5m.

$$n=-\frac{m}{1-5m}$$

Variable n cannot be equal to 0.

$$n=-\frac{m}{1-5m}\text{, }n\neq 0$$