Algebra Examples

$\frac{10 p}{p - q} + \frac{3 p}{q - p}$

Step 1

Simplify terms.

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Step 1.1

Factor $- 1$ out of $q$ .

$\frac{10 p}{p - q} + \frac{3 p}{- 1 (- q) - p}$

Step 1.2

Factor $- 1$ out of $- p$ .

$\frac{10 p}{p - q} + \frac{3 p}{- 1 (- q) - (p)}$

Step 1.3

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

$\frac{10 p}{p - q} + \frac{3 p}{- 1 (- q + p)}$

Step 1.4

Simplify the expression.

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Step 1.4.1

Move a negative from the denominator of $\frac{3 p}{- 1 (- q + p)}$ to the numerator.

$\frac{10 p}{p - q} + \frac{- (3 p)}{- q + p}$

Step 1.4.2

Reorder terms.

$\frac{10 p}{p - q} + \frac{- (3 p)}{p - q}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{10 p - (3 p)}{p - q}$

Step 2

Simplify the numerator.

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Step 2.1

Factor $p$ out of $10 p - 1 \cdot 3 p$ .

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Step 2.1.1

Factor $p$ out of $10 p$ .

$\frac{p \cdot 10 - 1 \cdot 3 p}{p - q}$

Step 2.1.2

Factor $p$ out of $- 1 \cdot 3 p$ .

$\frac{p \cdot 10 + p (- 1 \cdot 3)}{p - q}$

Step 2.1.3

Factor $p$ out of $p \cdot 10 + p (- 1 \cdot 3)$ .

$\frac{p (10 - 1 \cdot 3)}{p - q}$

Step 2.2

Multiply $- 1$ by $3$ .

$\frac{p (10 - 3)}{p - q}$

Step 2.3

Subtract $3$ from $10$ .

$\frac{p \cdot 7}{p - q}$

Step 3

Move $7$ to the left of $p$ .

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