Basic Math Examples

$\frac{a^{6} - 9 a^{4}}{3 a^{4}}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $a^{4}$ out of $a^{6} - 9 a^{4}$ .

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Step 1.1.1

Factor $a^{4}$ out of $a^{6}$ .

$\frac{a^{4} a^{2} - 9 a^{4}}{3 a^{4}}$

Step 1.1.2

Factor $a^{4}$ out of $- 9 a^{4}$ .

$\frac{a^{4} a^{2} + a^{4} \cdot - 9}{3 a^{4}}$

Step 1.1.3

Factor $a^{4}$ out of $a^{4} a^{2} + a^{4} \cdot - 9$ .

$\frac{a^{4} (a^{2} - 9)}{3 a^{4}}$

Step 1.2

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

$\frac{a^{4} (a^{2} - 3^{2})}{3 a^{4}}$

Step 1.3

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 $b = 3$ .

$\frac{a^{4} (a + 3) (a - 3)}{3 a^{4}}$

Step 2

Cancel the common factor of $a^{4}$ .

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Step 2.1

Cancel the common factor.

$\frac{a^{4} (a + 3) (a - 3)}{3 a^{4}}$

Step 2.2

Rewrite the expression.

$\frac{(a + 3) (a - 3)}{3}$