Algebra Examples

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

Step 1

Simplify terms.

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Step 1.1

Factor $- 1$ out of $p$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Simplify the expression.

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Step 1.4.1

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

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

Step 1.4.2

Reorder terms.

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 2

Simplify the numerator.

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Step 2.1

Multiply $- 1$ by $10$ .

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

Step 2.2

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

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Step 2.2.1

Factor $5$ out of $5 p$ .

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

Step 2.2.2

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

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

Step 2.2.3

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.

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Step 3.1

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

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Step 3.1.1

Factor $- 1$ out of $p$ .

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

Step 3.1.2

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

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

Step 3.1.3

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

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

Step 3.1.4

Cancel the common factor.

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

Step 3.1.5

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

$5 \cdot (- 1)$

Step 3.2

Multiply $5$ by $- 1$ .

$- 5$