Solve 3/x+2/m=1/n

$$\frac { 3 } { x } + \frac { 2 } { m } = \frac { 1 } { n }$$

Solve for m

$$m=-\frac{2nx}{3n-x}$$

$$n\neq 0\text{ and }x\neq 0\text{ and }x\neq 3n$$

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 mnx, the least common multiple of x,m,n.

$$mn\times 3+nx\times 2=mx$$

Subtract mx from both sides.

$$mn\times 3+nx\times 2-mx=0$$

Subtract nx\times 2 from both sides. Anything subtracted from zero gives its negation.

$$mn\times 3-mx=-nx\times 2$$

Multiply -1 and 2 to get -2.

$$mn\times 3-mx=-2nx$$

Combine all terms containing m.

$$\left(n\times 3-x\right)m=-2nx$$

The equation is in standard form.

$$\left(3n-x\right)m=-2nx$$

Divide both sides by 3n-x.

$$\frac{\left(3n-x\right)m}{3n-x}=-\frac{2nx}{3n-x}$$

Dividing by 3n-x undoes the multiplication by 3n-x.

$$m=-\frac{2nx}{3n-x}$$

Variable m cannot be equal to 0.

$$m=-\frac{2nx}{3n-x}\text{, }m\neq 0$$

Solve for n

$$n=\frac{mx}{2x+3m}$$

$$x\neq 0\text{ and }m\neq 0\text{ and }x\neq -\frac{3m}{2}$$

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 mnx, the least common multiple of x,m,n.

$$mn\times 3+nx\times 2=mx$$

Reorder the terms.

$$2nx+3mn=mx$$

Combine all terms containing n.

$$\left(2x+3m\right)n=mx$$

Divide both sides by 2x+3m.

$$\frac{\left(2x+3m\right)n}{2x+3m}=\frac{mx}{2x+3m}$$

Dividing by 2x+3m undoes the multiplication by 2x+3m.

$$n=\frac{mx}{2x+3m}$$

Variable n cannot be equal to 0.

$$n=\frac{mx}{2x+3m}\text{, }n\neq 0$$