Solve 7/p-1/q=3

$$\frac { 7 } { p } - \frac { 1 } { q } = 3$$

Solve for p

$$p=\frac{7q}{3q+1}$$

$$q\neq 0\text{ and }q\neq -\frac{1}{3}$$

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 pq, the least common multiple of p,q.

$$q\times 7-p=3pq$$

Subtract 3pq from both sides.

$$q\times 7-p-3pq=0$$

Subtract q\times 7 from both sides. Anything subtracted from zero gives its negation.

$$-p-3pq=-q\times 7$$

Multiply -1 and 7 to get -7.

$$-p-3pq=-7q$$

Combine all terms containing p.

$$\left(-1-3q\right)p=-7q$$

The equation is in standard form.

$$\left(-3q-1\right)p=-7q$$

Divide both sides by -1-3q.

$$\frac{\left(-3q-1\right)p}{-3q-1}=-\frac{7q}{-3q-1}$$

Dividing by -1-3q undoes the multiplication by -1-3q.

$$p=-\frac{7q}{-3q-1}$$

Divide -7q by -1-3q.

$$p=\frac{7q}{3q+1}$$

Variable p cannot be equal to 0.

$$p=\frac{7q}{3q+1}\text{, }p\neq 0$$

Solve for q

$$q=\frac{p}{7-3p}$$

$$p\neq 0\text{ and }p\neq \frac{7}{3}$$

Steps for Solving Linear Equation

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

$$q\times 7-p=3pq$$

Subtract 3pq from both sides.

$$q\times 7-p-3pq=0$$

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

$$q\times 7-3pq=p$$

Combine all terms containing q.

$$\left(7-3p\right)q=p$$

Divide both sides by 7-3p.

$$\frac{\left(7-3p\right)q}{7-3p}=\frac{p}{7-3p}$$

Dividing by 7-3p undoes the multiplication by 7-3p.

$$q=\frac{p}{7-3p}$$

Variable q cannot be equal to 0.

$$q=\frac{p}{7-3p}\text{, }q\neq 0$$