Solve 1/8=1/u+1/v

$$\frac { 1 } { 8 } = \frac { 1 } { u } + \frac { 1 } { v }$$

Solve for u

$$u=-\frac{8v}{8-v}$$

$$v\neq 0\text{ and }v\neq 8$$

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 8uv, the least common multiple of 8,u,v.

$$uv=8v+8u$$

Subtract 8u from both sides.

$$uv-8u=8v$$

Combine all terms containing u.

$$\left(v-8\right)u=8v$$

Divide both sides by v-8.

$$\frac{\left(v-8\right)u}{v-8}=\frac{8v}{v-8}$$

Dividing by v-8 undoes the multiplication by v-8.

$$u=\frac{8v}{v-8}$$

Variable u cannot be equal to 0.

$$u=\frac{8v}{v-8}\text{, }u\neq 0$$

Solve for v

$$v=-\frac{8u}{8-u}$$

$$u\neq 0\text{ and }u\neq 8$$

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 8uv, the least common multiple of 8,u,v.

$$uv=8v+8u$$

Subtract 8v from both sides.

$$uv-8v=8u$$

Combine all terms containing v.

$$\left(u-8\right)v=8u$$

Divide both sides by u-8.

$$\frac{\left(u-8\right)v}{u-8}=\frac{8u}{u-8}$$

Dividing by u-8 undoes the multiplication by u-8.

$$v=\frac{8u}{u-8}$$

Variable v cannot be equal to 0.

$$v=\frac{8u}{u-8}\text{, }v\neq 0$$