Solve x-n/m-x-m/n=m/n

$$\frac { x - n } { m } - \frac { x - m } { n } = \frac { m } { n }$$

Solve for m

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

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

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.

$$n\left(x-n\right)-m\left(x-m\right)=mm$$

Multiply m and m to get m^{2}.

$$n\left(x-n\right)-m\left(x-m\right)=m^{2}$$

Use the distributive property to multiply n by x-n.

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

Use the distributive property to multiply m by x-m.

$$nx-n^{2}-\left(mx-m^{2}\right)=m^{2}$$

To find the opposite of mx-m^{2}, find the opposite of each term.

$$nx-n^{2}-mx+m^{2}=m^{2}$$

Subtract m^{2} from both sides.

$$nx-n^{2}-mx+m^{2}-m^{2}=0$$

Combine m^{2} and -m^{2} to get 0.

$$nx-n^{2}-mx=0$$

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

$$-n^{2}-mx=-nx$$

Add n^{2} to both sides.

$$-mx=-nx+n^{2}$$

The equation is in standard form.

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

Divide both sides by -x.

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

Dividing by -x undoes the multiplication by -x.

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

Divide n\left(-x+n\right) by -x.

$$m=-\frac{n^{2}}{x}+n$$

Variable m cannot be equal to 0.

$$m=-\frac{n^{2}}{x}+n\text{, }m\neq 0$$

Solve for n (complex solution)

$$n=\frac{-\sqrt{x\left(x-4m\right)}+x}{2}$$

$$n=\frac{\sqrt{x\left(x-4m\right)}+x}{2}\text{, }m\neq 0\text{ and }x\neq 0$$

Solve for n

$$n=\frac{-\sqrt{x\left(x-4m\right)}+x}{2}$$

$$n=\frac{\sqrt{x\left(x-4m\right)}+x}{2}\text{, }m\neq 0\text{ and }\left(x>0\text{ or }x\leq 4m\right)\text{ and }\left(x<0\text{ or }x\geq 4m\right)\text{ and }\left(x=4m\text{ or }x\neq 0\right)$$