Solve 1/f=1/v+1/b

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

Solve for b

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

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

Steps for Solving Linear Equation

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

$$bv=bf+fv$$

Subtract bf from both sides.

$$bv-bf=fv$$

Combine all terms containing b.

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

Divide both sides by v-f.

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

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

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

Variable b cannot be equal to 0.

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

Solve for f

$$f=\frac{bv}{v+b}$$

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

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 bfv, the least common multiple of f,v,b.

$$bv=bf+fv$$

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

$$bf+fv=bv$$

Combine all terms containing f.

$$\left(b+v\right)f=bv$$

The equation is in standard form.

$$\left(v+b\right)f=bv$$

Divide both sides by b+v.

$$\frac{\left(v+b\right)f}{v+b}=\frac{bv}{v+b}$$

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

$$f=\frac{bv}{v+b}$$

Variable f cannot be equal to 0.

$$f=\frac{bv}{v+b}\text{, }f\neq 0$$