Solve n1/z-1/p=1/q

$$n \frac { 1 } { z } - \frac { 1 } { p } = \frac { 1 } { q }$$

Solve for n

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

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

Steps for Solving Linear Equation

Multiply both sides of the equation by pqz, the least common multiple of z,p,q.

$$npq\times 1-qz=pz$$

Add qz to both sides.

$$npq\times 1=pz+qz$$

Reorder the terms.

$$npq=pz+qz$$

The equation is in standard form.

$$pqn=pz+qz$$

Divide both sides by pq.

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

Dividing by pq undoes the multiplication by pq.

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

Divide z\left(p+q\right) by pq.

$$n=\frac{z}{p}+\frac{z}{q}$$

Solve for p

$$p=\frac{qz}{nq-z}$$

$$z\neq 0\text{ and }q\neq 0\text{ and }n\neq \frac{z}{q}\text{ and }z\neq nq$$

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 pqz, the least common multiple of z,p,q.

$$npq\times 1-qz=pz$$

Subtract pz from both sides.

$$npq\times 1-qz-pz=0$$

Add qz to both sides. Anything plus zero gives itself.

$$npq\times 1-pz=qz$$

Reorder the terms.

$$-pz+npq=qz$$

Combine all terms containing p.

$$\left(-z+nq\right)p=qz$$

The equation is in standard form.

$$\left(nq-z\right)p=qz$$

Divide both sides by -z+nq.

$$\frac{\left(nq-z\right)p}{nq-z}=\frac{qz}{nq-z}$$

Dividing by -z+nq undoes the multiplication by -z+nq.

$$p=\frac{qz}{nq-z}$$

Variable p cannot be equal to 0.

$$p=\frac{qz}{nq-z}\text{, }p\neq 0$$