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.

$$p=-\frac{Fq}{F-q}\text{, }p\neq 0$$