Solve 1/v-1/w=1/x

$$\frac { 1 } { v } - \frac { 1 } { w } = \frac { 1 } { x }$$

Solve for v

$$v=\frac{wx}{x+w}$$

$$w\neq 0\text{ and }x\neq 0\text{ and }w\neq -x$$

Steps for Solving Linear Equation

Variable v cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by vwx, the least common multiple of v,w,x.

$$wx-vx=vw$$

Subtract vw from both sides.

$$wx-vx-vw=0$$

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

$$-vx-vw=-wx$$

Combine all terms containing v.

$$\left(-x-w\right)v=-wx$$

Divide both sides by -x-w.

$$\frac{\left(-x-w\right)v}{-x-w}=-\frac{wx}{-x-w}$$

Dividing by -x-w undoes the multiplication by -x-w.

$$v=-\frac{wx}{-x-w}$$

Divide -wx by -x-w.

$$v=\frac{wx}{x+w}$$

Variable v cannot be equal to 0.

$$v=\frac{wx}{x+w}\text{, }v\neq 0$$

Solve for w

$$w=\frac{vx}{x-v}$$

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

Steps for Solving Linear Equation

Variable w cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by vwx, the least common multiple of v,w,x.

$$wx-vx=vw$$

Subtract vw from both sides.

$$wx-vx-vw=0$$

Add vx to both sides. Anything plus zero gives itself.

$$wx-vw=vx$$

Combine all terms containing w.

$$\left(x-v\right)w=vx$$

Divide both sides by x-v.

$$\frac{\left(x-v\right)w}{x-v}=\frac{vx}{x-v}$$

Dividing by x-v undoes the multiplication by x-v.

$$w=\frac{vx}{x-v}$$

Variable w cannot be equal to 0.

$$w=\frac{vx}{x-v}\text{, }w\neq 0$$