Solve 1/u=f+v/fv

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

Solve for f

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

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

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 u,fv.

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

Use the distributive property to multiply u by f+v.

$$fv=uf+uv$$

Subtract uf from both sides.

$$fv-uf=uv$$

Combine all terms containing f.

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

Divide both sides by -u+v.

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

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

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

Variable f cannot be equal to 0.

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

Solve for u

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

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

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 u,fv.

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

Use the distributive property to multiply u by f+v.

$$fv=uf+uv$$

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

$$uf+uv=fv$$

Combine all terms containing u.

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

The equation is in standard form.

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

Divide both sides by f+v.

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

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

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

Variable u cannot be equal to 0.

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