Basic Math Examples

$\frac{\frac{a^{2} - b^{2}}{a^{2} + b^{2}}}{\frac{15 a - 15 b}{3 a^{2} + 3 b^{2}}}$

Step 1

Cancel the common factor of $15 a - 15 b$ and $3 a^{2} + 3 b^{2}$ .

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Step 1.1

Factor $3$ out of $15 a$ .

$\frac{\frac{a^{2} - b^{2}}{a^{2} + b^{2}}}{\frac{3 (5 a) - 15 b}{3 a^{2} + 3 b^{2}}}$

Step 1.2

Factor $3$ out of $- 15 b$ .

$\frac{\frac{a^{2} - b^{2}}{a^{2} + b^{2}}}{\frac{3 (5 a) + 3 (- 5 b)}{3 a^{2} + 3 b^{2}}}$

Step 1.3

Factor $3$ out of $3 (5 a) + 3 (- 5 b)$ .

$\frac{\frac{a^{2} - b^{2}}{a^{2} + b^{2}}}{\frac{3 (5 a - 5 b)}{3 a^{2} + 3 b^{2}}}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $3$ out of $3 a^{2}$ .

$\frac{\frac{a^{2} - b^{2}}{a^{2} + b^{2}}}{\frac{3 (5 a - 5 b)}{3 (a^{2}) + 3 b^{2}}}$

Step 1.4.2

Factor $3$ out of $3 b^{2}$ .

$\frac{\frac{a^{2} - b^{2}}{a^{2} + b^{2}}}{\frac{3 (5 a - 5 b)}{3 (a^{2}) + 3 (b^{2})}}$

Step 1.4.3

Factor $3$ out of $3 (a^{2}) + 3 (b^{2})$ .

$\frac{\frac{a^{2} - b^{2}}{a^{2} + b^{2}}}{\frac{3 (5 a - 5 b)}{3 (a^{2} + b^{2})}}$

Step 1.4.4

Cancel the common factor.

$\frac{\frac{a^{2} - b^{2}}{a^{2} + b^{2}}}{\frac{3 (5 a - 5 b)}{3 (a^{2} + b^{2})}}$

Step 1.4.5

Rewrite the expression.

$\frac{\frac{a^{2} - b^{2}}{a^{2} + b^{2}}}{\frac{5 a - 5 b}{a^{2} + b^{2}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{a^{2} - b^{2}}{a^{2} + b^{2}} \cdot \frac{a^{2} + b^{2}}{5 a - 5 b}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $a^{2} + b^{2}$ .

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Step 3.1.1

Cancel the common factor.

$\frac{a^{2} - b^{2}}{a^{2} + b^{2}} \cdot \frac{a^{2} + b^{2}}{5 a - 5 b}$

Step 3.1.2

Rewrite the expression.

$(a^{2} - b^{2}) \frac{1}{5 a - 5 b}$

Step 3.2

Factor $5$ out of $5 a - 5 b$ .

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Step 3.2.1

Factor $5$ out of $5 a$ .

$(a^{2} - b^{2}) \frac{1}{5 (a) - 5 b}$

Step 3.2.2

Factor $5$ out of $- 5 b$ .

$(a^{2} - b^{2}) \frac{1}{5 (a) + 5 (- b)}$

Step 3.2.3

Factor $5$ out of $5 (a) + 5 (- b)$ .

$(a^{2} - b^{2}) \frac{1}{5 (a - b)}$

Step 3.3

Multiply $a^{2} - b^{2}$ by $\frac{1}{5 (a - b)}$ .

$\frac{a^{2} - b^{2}}{5 (a - b)}$

Step 4

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

$\frac{(a + b) (a - b)}{5 (a - b)}$

Step 5

Cancel the common factor of $a - b$ .

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Step 5.1

Cancel the common factor.

$\frac{(a + b) (a - b)}{5 (a - b)}$

Step 5.2

Rewrite the expression.

$\frac{a + b}{5}$