Solve 1/3*30/x+1/3*30-n/x-m=1

$$\frac { 1 } { 3 } \times \frac { 30 } { x } + \frac { 1 } { 3 } \times \frac { 30 - n } { x - m } = 1$$

Solve for n

$$n=3m-3x-\frac{30m}{x}+60$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 3x\left(-x+m\right), the least common multiple of 3,x,x-m.

$$\frac{1}{3}\left(-3x+3m\right)\times 30+\frac{1}{3}\left(-3\right)x\left(30-n\right)=3x\left(-x+m\right)$$

Multiply \frac{1}{3} and 30 to get 10.

$$10\left(-3x+3m\right)+\frac{1}{3}\left(-3\right)x\left(30-n\right)=3x\left(-x+m\right)$$

Use the distributive property to multiply 10 by -3x+3m.

$$-30x+30m+\frac{1}{3}\left(-3\right)x\left(30-n\right)=3x\left(-x+m\right)$$

Multiply \frac{1}{3} and -3 to get -1.

$$-30x+30m-x\left(30-n\right)=3x\left(-x+m\right)$$

Use the distributive property to multiply -x by 30-n.

$$-30x+30m-30x+xn=3x\left(-x+m\right)$$

Combine -30x and -30x to get -60x.

$$-60x+30m+xn=3x\left(-x+m\right)$$

Use the distributive property to multiply 3x by -x+m.

$$-60x+30m+xn=-3x^{2}+3xm$$

Add 60x to both sides.

$$30m+xn=-3x^{2}+3xm+60x$$

Subtract 30m from both sides.

$$xn=-3x^{2}+3xm+60x-30m$$

The equation is in standard form.

$$xn=-3x^{2}+3mx+60x-30m$$

Divide both sides by x.

$$\frac{xn}{x}=\frac{-3x^{2}+3mx+60x-30m}{x}$$

Dividing by x undoes the multiplication by x.

$$n=\frac{-3x^{2}+3mx+60x-30m}{x}$$

Divide 60x-30m+3xm-3x^{2} by x.

$$n=3m-3x-\frac{30m}{x}+60$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{x\left(60-n-3x\right)}{3\left(x-10\right)}\text{, }&n\neq 30\text{ and }x\neq 0\text{ and }x\neq 10\\m\neq 10\text{, }&n=30\text{ and }x=10\end{matrix}\right.$$