Solve 1/f=1/u+1/v

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

Solve for f

$$f=\frac{uv}{u+v}$$

$$v\neq 0\text{ and }u\neq 0\text{ and }u\neq -v$$

Steps for Solving Linear Equation

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

$$uv=fv+fu$$

Swap sides so that all variable terms are on the left hand side.

$$fv+fu=uv$$

Combine all terms containing f.

$$\left(v+u\right)f=uv$$

The equation is in standard form.

$$\left(u+v\right)f=uv$$

Divide both sides by v+u.

$$\frac{\left(u+v\right)f}{u+v}=\frac{uv}{u+v}$$

Dividing by v+u undoes the multiplication by v+u.

$$f=\frac{uv}{u+v}$$

Variable f cannot be equal to 0.

$$f=\frac{uv}{u+v}\text{, }f\neq 0$$

Solve for u

$$u=-\frac{fv}{f-v}$$

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

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 fuv, the least common multiple of f,u,v.

$$uv=fv+fu$$

Subtract fu from both sides.

$$uv-fu=fv$$

Combine all terms containing u.

$$\left(v-f\right)u=fv$$

Divide both sides by v-f.

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

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

$$u=\frac{fv}{v-f}$$

Variable u cannot be equal to 0.

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