Basic Math Examples

$\frac{9 a^{2} - 64}{a^{2} - 4} \div \frac{3 a - 8}{a - 2}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{9 a^{2} - 64}{a^{2} - 4} \cdot \frac{a - 2}{3 a - 8}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $9 a^{2}$ as ${(3 a)}^{2}$ .

$\frac{{(3 a)}^{2} - 64}{a^{2} - 4} \cdot \frac{a - 2}{3 a - 8}$

Step 2.2

Rewrite $64$ as $8^{2}$ .

$\frac{{(3 a)}^{2} - 8^{2}}{a^{2} - 4} \cdot \frac{a - 2}{3 a - 8}$

Step 2.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 a$ and $b = 8$ .

$\frac{(3 a + 8) (3 a - 8)}{a^{2} - 4} \cdot \frac{a - 2}{3 a - 8}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $4$ as $2^{2}$ .

$\frac{(3 a + 8) (3 a - 8)}{a^{2} - 2^{2}} \cdot \frac{a - 2}{3 a - 8}$

Step 3.2

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 $b = 2$ .

$\frac{(3 a + 8) (3 a - 8)}{(a + 2) (a - 2)} \cdot \frac{a - 2}{3 a - 8}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $3 a - 8$ .

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Step 4.1.1

Factor $3 a - 8$ out of $(3 a + 8) (3 a - 8)$ .

$\frac{(3 a - 8) (3 a + 8)}{(a + 2) (a - 2)} \cdot \frac{a - 2}{3 a - 8}$

Step 4.1.2

Cancel the common factor.

$\frac{(3 a - 8) (3 a + 8)}{(a + 2) (a - 2)} \cdot \frac{a - 2}{3 a - 8}$

Step 4.1.3

Rewrite the expression.

$\frac{3 a + 8}{(a + 2) (a - 2)} (a - 2)$

Step 4.2

Cancel the common factor of $a - 2$ .

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Step 4.2.1

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

$\frac{3 a + 8}{(a - 2) (a + 2)} (a - 2)$

Step 4.2.2

Cancel the common factor.

$\frac{3 a + 8}{(a - 2) (a + 2)} (a - 2)$

Step 4.2.3

Rewrite the expression.

$\frac{3 a + 8}{a + 2}$