Solve 1/p+1/q=1/f

$$\frac { 1 } { p } + \frac { 1 } { q } = \frac { 1 } { f }$$

Solve for f

$$f=\frac{pq}{p+q}$$

$$p\neq 0\text{ and }q\neq 0\text{ and }p\neq -q$$

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 fpq, the least common multiple of p,q,f.

$$fq+fp=pq$$

Combine all terms containing f.

$$\left(q+p\right)f=pq$$

The equation is in standard form.

$$\left(p+q\right)f=pq$$

Divide both sides by p+q.

$$\frac{\left(p+q\right)f}{p+q}=\frac{pq}{p+q}$$

Dividing by p+q undoes the multiplication by p+q.

$$f=\frac{pq}{p+q}$$

Variable f cannot be equal to 0.

$$f=\frac{pq}{p+q}\text{, }f\neq 0$$

Solve for p

$$p=-\frac{fq}{f-q}$$

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

Steps for Solving Linear Equation

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

$$fq+fp=pq$$

Subtract pq from both sides.

$$fq+fp-pq=0$$

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

$$fp-pq=-fq$$

Combine all terms containing p.

$$\left(f-q\right)p=-fq$$

Divide both sides by f-q.

$$\frac{\left(f-q\right)p}{f-q}=-\frac{fq}{f-q}$$

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

$$p=-\frac{fq}{f-q}$$

Variable p cannot be equal to 0.

$$p=-\frac{fq}{f-q}\text{, }p\neq 0$$