Solve 1/x=1/u+1/v

$$\frac{ 1 }{ x } = \frac{ 1 }{ u } + \frac{ 1 }{ v }$$

Solve for u

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

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

Steps for Solving Linear Equation

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

$$uv=vx+ux$$

Subtract ux from both sides.

$$uv-ux=vx$$

Combine all terms containing u.

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

Divide both sides by -x+v.

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

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

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

Variable u cannot be equal to 0.

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

Solve for v

$$v=-\frac{ux}{x-u}$$

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

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 uvx, the least common multiple of x,u,v.

$$uv=vx+ux$$

Subtract vx from both sides.

$$uv-vx=ux$$

Combine all terms containing v.

$$\left(u-x\right)v=ux$$

Divide both sides by -x+u.

$$\frac{\left(u-x\right)v}{u-x}=\frac{ux}{u-x}$$

Dividing by -x+u undoes the multiplication by -x+u.

$$v=\frac{ux}{u-x}$$

Variable v cannot be equal to 0.

$$v=\frac{ux}{u-x}\text{, }v\neq 0$$