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

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

Solve for f

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

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

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 u,v,f.

$$fv+fu=uv$$

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 u+v.

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

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

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

Variable f cannot be equal to 0.

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

Solve for u

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

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

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 u,v,f.

$$fv+fu=uv$$

Subtract uv from both sides.

$$fv+fu-uv=0$$

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

$$fu-uv=-fv$$

Combine all terms containing u.

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

Divide both sides by f-v.

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

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

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

Variable u cannot be equal to 0.

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