Solve 1/m+1/n=4/7

$$\frac { 1 } { m } + \frac { 1 } { n } = \frac { 4 } { 7 }$$

Solve for m

$$m=-\frac{7n}{7-4n}$$

$$n\neq 0\text{ and }n\neq \frac{7}{4}$$

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 7mn, the least common multiple of m,n,7.

$$7n+7m=4mn$$

Subtract 4mn from both sides.

$$7n+7m-4mn=0$$

Subtract 7n from both sides. Anything subtracted from zero gives its negation.

$$7m-4mn=-7n$$

Combine all terms containing m.

$$\left(7-4n\right)m=-7n$$

Divide both sides by 7-4n.

$$\frac{\left(7-4n\right)m}{7-4n}=-\frac{7n}{7-4n}$$

Dividing by 7-4n undoes the multiplication by 7-4n.

$$m=-\frac{7n}{7-4n}$$

Variable m cannot be equal to 0.

$$m=-\frac{7n}{7-4n}\text{, }m\neq 0$$

Solve for n

$$n=-\frac{7m}{7-4m}$$

$$m\neq 0\text{ and }m\neq \frac{7}{4}$$

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 7mn, the least common multiple of m,n,7.

$$7n+7m=4mn$$

Subtract 4mn from both sides.

$$7n+7m-4mn=0$$

Subtract 7m from both sides. Anything subtracted from zero gives its negation.

$$7n-4mn=-7m$$

Combine all terms containing n.

$$\left(7-4m\right)n=-7m$$

Divide both sides by 7-4m.

$$\frac{\left(7-4m\right)n}{7-4m}=-\frac{7m}{7-4m}$$

Dividing by 7-4m undoes the multiplication by 7-4m.

$$n=-\frac{7m}{7-4m}$$

Variable n cannot be equal to 0.

$$n=-\frac{7m}{7-4m}\text{, }n\neq 0$$