Basic Math Examples

$\frac{2 a - 10}{a^{2} - 36} \cdot \frac{a - 6}{3 a - 15}$

Step 1

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

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Step 1.1

Factor $2$ out of $2 a$ .

$\frac{2 (a) - 10}{a^{2} - 36} \cdot \frac{a - 6}{3 a - 15}$

Step 1.2

Factor $2$ out of $- 10$ .

$\frac{2 a + 2 \cdot - 5}{a^{2} - 36} \cdot \frac{a - 6}{3 a - 15}$

Step 1.3

Factor $2$ out of $2 a + 2 \cdot - 5$ .

$\frac{2 (a - 5)}{a^{2} - 36} \cdot \frac{a - 6}{3 a - 15}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{2 (a - 5)}{a^{2} - 6^{2}} \cdot \frac{a - 6}{3 a - 15}$

Step 2.2

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 $b = 6$ .

$\frac{2 (a - 5)}{(a + 6) (a - 6)} \cdot \frac{a - 6}{3 a - 15}$

Step 3

Simplify terms.

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Step 3.1

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

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Step 3.1.1

Factor $3$ out of $3 a$ .

$\frac{2 (a - 5)}{(a + 6) (a - 6)} \cdot \frac{a - 6}{3 (a) - 15}$

Step 3.1.2

Factor $3$ out of $- 15$ .

$\frac{2 (a - 5)}{(a + 6) (a - 6)} \cdot \frac{a - 6}{3 a + 3 \cdot - 5}$

Step 3.1.3

Factor $3$ out of $3 a + 3 \cdot - 5$ .

$\frac{2 (a - 5)}{(a + 6) (a - 6)} \cdot \frac{a - 6}{3 (a - 5)}$

Step 3.2

Cancel the common factor of $a - 5$ .

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Step 3.2.1

Factor $a - 5$ out of $2 (a - 5)$ .

$\frac{(a - 5) \cdot 2}{(a + 6) (a - 6)} \cdot \frac{a - 6}{3 (a - 5)}$

Step 3.2.2

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

$\frac{(a - 5) \cdot 2}{(a + 6) (a - 6)} \cdot \frac{a - 6}{(a - 5) \cdot 3}$

Step 3.2.3

Cancel the common factor.

$\frac{(a - 5) \cdot 2}{(a + 6) (a - 6)} \cdot \frac{a - 6}{(a - 5) \cdot 3}$

Step 3.2.4

Rewrite the expression.

$\frac{2}{(a + 6) (a - 6)} \cdot \frac{a - 6}{3}$

Step 3.3

Cancel the common factor of $a - 6$ .

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Step 3.3.1

Factor $a - 6$ out of $(a + 6) (a - 6)$ .

$\frac{2}{(a - 6) (a + 6)} \cdot \frac{a - 6}{3}$

Step 3.3.2

Cancel the common factor.

$\frac{2}{(a - 6) (a + 6)} \cdot \frac{a - 6}{3}$

Step 3.3.3

Rewrite the expression.

$\frac{2}{a + 6} \cdot \frac{1}{3}$

Step 3.4

Multiply $\frac{2}{a + 6}$ by $\frac{1}{3}$ .

$\frac{2}{(a + 6) \cdot 3}$

Step 3.5

Move $3$ to the left of $a + 6$ .

$\frac{2}{3 (a + 6)}$