Algebra Examples

$\frac{m x^{2} - m y^{2}}{2 m + 8} \cdot \frac{3 m + 12}{m y + m x}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $m$ out of $m x^{2} - m y^{2}$ .

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Step 1.1.1

Factor $m$ out of $m x^{2}$ .

$\frac{m (x^{2}) - m y^{2}}{2 m + 8} \cdot \frac{3 m + 12}{m y + m x}$

Step 1.1.2

Factor $m$ out of $- m y^{2}$ .

$\frac{m (x^{2}) + m (- 1 y^{2})}{2 m + 8} \cdot \frac{3 m + 12}{m y + m x}$

Step 1.1.3

Factor $m$ out of $m (x^{2}) + m (- 1 y^{2})$ .

$\frac{m (x^{2} - 1 y^{2})}{2 m + 8} \cdot \frac{3 m + 12}{m y + m x}$

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = y$ .

$\frac{m (x + y) (x - y)}{2 m + 8} \cdot \frac{3 m + 12}{m y + m x}$

Step 2

Simplify terms.

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Step 2.1

Factor $2$ out of $2 m + 8$ .

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Step 2.1.1

Factor $2$ out of $2 m$ .

$\frac{m (x + y) (x - y)}{2 (m) + 8} \cdot \frac{3 m + 12}{m y + m x}$

Step 2.1.2

Factor $2$ out of $8$ .

$\frac{m (x + y) (x - y)}{2 m + 2 \cdot 4} \cdot \frac{3 m + 12}{m y + m x}$

Step 2.1.3

Factor $2$ out of $2 m + 2 \cdot 4$ .

$\frac{m (x + y) (x - y)}{2 (m + 4)} \cdot \frac{3 m + 12}{m y + m x}$

Step 2.2

Factor $3$ out of $3 m + 12$ .

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Step 2.2.1

Factor $3$ out of $3 m$ .

$\frac{m (x + y) (x - y)}{2 (m + 4)} \cdot \frac{3 (m) + 12}{m y + m x}$

Step 2.2.2

Factor $3$ out of $12$ .

$\frac{m (x + y) (x - y)}{2 (m + 4)} \cdot \frac{3 m + 3 \cdot 4}{m y + m x}$

Step 2.2.3

Factor $3$ out of $3 m + 3 \cdot 4$ .

$\frac{m (x + y) (x - y)}{2 (m + 4)} \cdot \frac{3 (m + 4)}{m y + m x}$

Step 2.3

Factor $m$ out of $m y + m x$ .

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Step 2.3.1

Factor $m$ out of $m y$ .

$\frac{m (x + y) (x - y)}{2 (m + 4)} \cdot \frac{3 (m + 4)}{m (y) + m x}$

Step 2.3.2

Factor $m$ out of $m x$ .

$\frac{m (x + y) (x - y)}{2 (m + 4)} \cdot \frac{3 (m + 4)}{m (y) + m (x)}$

Step 2.3.3

Factor $m$ out of $m (y) + m (x)$ .

$\frac{m (x + y) (x - y)}{2 (m + 4)} \cdot \frac{3 (m + 4)}{m (y + x)}$

Step 2.4

Cancel the common factor of $m$ .

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Step 2.4.1

Factor $m$ out of $m (x + y) (x - y)$ .

$\frac{m ((x + y) (x - y))}{2 (m + 4)} \cdot \frac{3 (m + 4)}{m (y + x)}$

Step 2.4.2

Cancel the common factor.

$\frac{m ((x + y) (x - y))}{2 (m + 4)} \cdot \frac{3 (m + 4)}{m (y + x)}$

Step 2.4.3

Rewrite the expression.

$\frac{(x + y) (x - y)}{2 (m + 4)} \cdot \frac{3 (m + 4)}{y + x}$

Step 2.5

Cancel the common factor of $m + 4$ .

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Step 2.5.1

Factor $m + 4$ out of $2 (m + 4)$ .

$\frac{(x + y) (x - y)}{(m + 4) \cdot 2} \cdot \frac{3 (m + 4)}{y + x}$

Step 2.5.2

Factor $m + 4$ out of $3 (m + 4)$ .

$\frac{(x + y) (x - y)}{(m + 4) \cdot 2} \cdot \frac{(m + 4) \cdot 3}{y + x}$

Step 2.5.3

Cancel the common factor.

$\frac{(x + y) (x - y)}{(m + 4) \cdot 2} \cdot \frac{(m + 4) \cdot 3}{y + x}$

Step 2.5.4

Rewrite the expression.

$\frac{(x + y) (x - y)}{2} \cdot \frac{3}{y + x}$

Step 2.6

Multiply $\frac{(x + y) (x - y)}{2}$ by $\frac{3}{y + x}$ .

$\frac{(x + y) (x - y) \cdot 3}{2 (y + x)}$

Step 2.7

Cancel the common factor of $x + y$ and $y + x$ .

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Step 2.7.1

Reorder terms.

$\frac{(x + y) (x - y) \cdot 3}{2 (x + y)}$

Step 2.7.2

Cancel the common factor.

$\frac{(x + y) (x - y) \cdot 3}{2 (x + y)}$

Step 2.7.3

Rewrite the expression.

$\frac{(x - y) \cdot 3}{2}$

Step 2.8

Move $3$ to the left of $x - y$ .

$\frac{3 (x - y)}{2}$