Simplify (5p)/(2q-p)+(10q)/(p-2q)

$\frac{5 p}{2 q - p} + \frac{10 q}{p - 2 q}$

Step 1

Simplify terms.

Factor $- 1$ out of $p$ .

$\frac{5 p}{2 q - p} + \frac{10 q}{- 1 (- p) - 2 q}$

Factor $- 1$ out of $- 2 q$ .

$\frac{5 p}{2 q - p} + \frac{10 q}{- 1 (- p) - (2 q)}$

Factor $- 1$ out of $- 1 (- p) - (2 q)$ .

$\frac{5 p}{2 q - p} + \frac{10 q}{- 1 (- p + 2 q)}$

Simplify the expression.

Move a negative from the denominator of $\frac{10 q}{- 1 (- p + 2 q)}$ to the numerator.

$\frac{5 p}{2 q - p} + \frac{- (10 q)}{- p + 2 q}$

Reorder terms.

$\frac{5 p}{- p + 2 q} + \frac{- (10 q)}{- p + 2 q}$

Combine the numerators over the common denominator.

$\frac{5 p - (10 q)}{- p + 2 q}$

Step 2

Simplify the numerator.

Multiply $- 1$ by $10$ .

$\frac{5 p - 10 q}{- p + 2 q}$

Factor $5$ out of $5 p - 10 q$ .

Factor $5$ out of $5 p$ .

$\frac{5 (p) - 10 q}{- p + 2 q}$

Factor $5$ out of $- 10 q$ .

$\frac{5 (p) + 5 (- 2 q)}{- p + 2 q}$

Factor $5$ out of $5 (p) + 5 (- 2 q)$ .

$\frac{5 (p - 2 q)}{- p + 2 q}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $p - 2 q$ and $- p + 2 q$ .

Factor $- 1$ out of $p$ .

$\frac{5 (- 1 (- p) - 2 q)}{- p + 2 q}$

Factor $- 1$ out of $- 2 q$ .

$\frac{5 (- 1 (- p) - (2 q))}{- p + 2 q}$

Factor $- 1$ out of $- 1 (- p) - (2 q)$ .

$\frac{5 (- 1 (- p + 2 q))}{- p + 2 q}$

Cancel the common factor.

$\frac{5 (- 1 (- p + 2 q))}{- p + 2 q}$

Divide $5 \cdot (- 1)$ by $1$ .

$5 \cdot (- 1)$

Multiply $5$ by $- 1$ .

$- 5$