Solve -(-p/q)=p/q+0

$$- ( - \frac { p } { q } ) = \frac { p } { q } + 0$$

Solve for p

$$p\in \mathrm{R}$$

$$q\neq 0$$

Solution Steps

Multiply both sides of the equation by q.

$$-q\left(-\frac{p}{q}\right)=p+0$$

Express q\left(-\frac{p}{q}\right) as a single fraction.

$$-\frac{-qp}{q}=p+0$$

Cancel out q in both numerator and denominator.

$$-\left(-p\right)=p+0$$

The opposite of -p is p.

$$p=p+0$$

Anything plus zero gives itself.

$$p=p$$

Subtract p from both sides.

$$p-p=0$$

Combine p and -p to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any p.

$$p\in \mathrm{R}$$

Solve for q

$$q\neq 0$$

Solution Steps

Variable q cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by q.

$$-q\left(-\frac{p}{q}\right)=p+0$$

Express q\left(-\frac{p}{q}\right) as a single fraction.

$$-\frac{-qp}{q}=p+0$$

Anything plus zero gives itself.

$$-\frac{-qp}{q}=p$$

Variable q cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by q.

$$qp=pq$$

Reorder the terms.

$$\text{true}$$

This is true for any q.

$$q\in \mathrm{R}$$

Variable q cannot be equal to 0.

$$q\in \mathrm{R}\setminus 0$$