Basic Math Examples

$\frac{\frac{\frac{a - 3^{2}}{a^{2} - 5}}{9 - a^{2}}}{2 a - 10}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{\frac{a - 3^{2}}{a^{2} - 5}}{9 - a^{2}} \cdot \frac{1}{2 a - 10}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{a - 3^{2}}{a^{2} - 5} \cdot \frac{1}{9 - a^{2}} \frac{1}{2 a - 10}$

Step 3

Simplify the numerator.

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Step 3.1

Raise $3$ to the power of $2$ .

$\frac{a - 1 \cdot 9}{a^{2} - 5} \cdot \frac{1}{9 - a^{2}} \frac{1}{2 a - 10}$

Step 3.2

Multiply $- 1$ by $9$ .

$\frac{a - 9}{a^{2} - 5} \cdot \frac{1}{9 - a^{2}} \frac{1}{2 a - 10}$

Step 4

Simplify the denominator.

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Step 4.1

Rewrite $9$ as $3^{2}$ .

$\frac{a - 9}{a^{2} - 5} \cdot \frac{1}{3^{2} - a^{2}} \frac{1}{2 a - 10}$

Step 4.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3$ and $b = a$ .

$\frac{a - 9}{a^{2} - 5} \cdot \frac{1}{(3 + a) (3 - a)} \frac{1}{2 a - 10}$

Step 5

Simplify terms.

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Step 5.1

Multiply $\frac{a - 9}{a^{2} - 5}$ by $\frac{1}{(3 + a) (3 - a)}$ .

$\frac{a - 9}{(a^{2} - 5) ((3 + a) (3 - a))} \cdot \frac{1}{2 a - 10}$

Step 5.2

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

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Step 5.2.1

Factor $2$ out of $2 a$ .

$\frac{a - 9}{(a^{2} - 5) (3 + a) (3 - a)} \cdot \frac{1}{2 (a) - 10}$

Step 5.2.2

Factor $2$ out of $- 10$ .

$\frac{a - 9}{(a^{2} - 5) (3 + a) (3 - a)} \cdot \frac{1}{2 a + 2 \cdot - 5}$

Step 5.2.3

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

$\frac{a - 9}{(a^{2} - 5) (3 + a) (3 - a)} \cdot \frac{1}{2 (a - 5)}$

Step 5.3

Multiply $\frac{a - 9}{(a^{2} - 5) (3 + a) (3 - a)}$ by $\frac{1}{2 (a - 5)}$ .

$\frac{a - 9}{(a^{2} - 5) (3 + a) (3 - a) (2 (a - 5))}$

Step 5.4

Move $2$ to the left of $(a^{2} - 5) (3 + a) (3 - a)$ .

$\frac{a - 9}{2 (a^{2} - 5) (3 + a) (3 - a) (a - 5)}$