Basic Math Examples

$\frac{a^{2} - 36}{10 a} \cdot (\frac{2 a}{a + 6})$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $36$ as $6^{2}$ .

$\frac{a^{2} - 6^{2}}{10 a} \cdot \frac{2 a}{a + 6}$

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 $a = a$ and $b = 6$ .

$\frac{(a + 6) (a - 6)}{10 a} \cdot \frac{2 a}{a + 6}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $a + 6$ .

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Step 2.1.1

Cancel the common factor.

$\frac{(a + 6) (a - 6)}{10 a} \cdot \frac{2 a}{a + 6}$

Step 2.1.2

Rewrite the expression.

$\frac{a - 6}{10 a} \cdot (2 a)$

Step 2.2

Cancel the common factor of $2 a$ .

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Step 2.2.1

Factor $2 a$ out of $10 a$ .

$\frac{a - 6}{2 a (5)} \cdot (2 a)$

Step 2.2.2

Cancel the common factor.

$\frac{a - 6}{2 a \cdot 5} \cdot (2 a)$

Step 2.2.3

Rewrite the expression.

$\frac{a - 6}{5}$