Solve n1/u+1/v=1/f

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

Solve for f

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

$$u\neq 0\text{ and }v\neq 0\text{ and }n\neq -\frac{u}{v}\text{ and }u\neq -nv$$

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.

$$nfv\times 1+fu=uv$$

Reorder the terms.

$$fnv+fu=uv$$

Combine all terms containing f.

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

Divide both sides by nv+u.

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

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

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

Variable f cannot be equal to 0.

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

Solve for n

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

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

Steps for Solving Linear Equation

Multiply both sides of the equation by fuv, the least common multiple of u,v,f.

$$nfv\times 1+fu=uv$$

Subtract fu from both sides.

$$nfv\times 1=uv-fu$$

Reorder the terms.

$$fnv=uv-fu$$

The equation is in standard form.

$$fvn=uv-fu$$

Divide both sides by fv.

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

Dividing by fv undoes the multiplication by fv.

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

Divide u\left(v-f\right) by fv.

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