Basic Math Examples

$\frac{z^{2} - 64}{z} \div \frac{z + 8}{z + 9}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{z^{2} - 64}{z} \cdot \frac{z + 9}{z + 8}$

Step 2

Simplify the numerator.

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Step 2.1

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

$\frac{z^{2} - 8^{2}}{z} \cdot \frac{z + 9}{z + 8}$

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 $a = z$ and $b = 8$ .

$\frac{(z + 8) (z - 8)}{z} \cdot \frac{z + 9}{z + 8}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $z + 8$ .

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Step 3.1.1

Cancel the common factor.

$\frac{(z + 8) (z - 8)}{z} \cdot \frac{z + 9}{z + 8}$

Step 3.1.2

Rewrite the expression.

$\frac{z - 8}{z} (z + 9)$

Step 3.2

Multiply $\frac{z - 8}{z}$ by $z + 9$ .

$\frac{(z - 8) (z + 9)}{z}$