Basic Math Examples

$\frac{z^{2} - 25}{3 z - 15}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $25$ as $5^{2}$ .

$\frac{z^{2} - 5^{2}}{3 z - 15}$

Step 1.2

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 $b = 5$ .

$\frac{(z + 5) (z - 5)}{3 z - 15}$

Step 2

Simplify terms.

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Step 2.1

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

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Step 2.1.1

Factor $3$ out of $3 z$ .

$\frac{(z + 5) (z - 5)}{3 (z) - 15}$

Step 2.1.2

Factor $3$ out of $- 15$ .

$\frac{(z + 5) (z - 5)}{3 z + 3 \cdot - 5}$

Step 2.1.3

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

$\frac{(z + 5) (z - 5)}{3 (z - 5)}$

Step 2.2

Cancel the common factor of $z - 5$ .

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Step 2.2.1

Cancel the common factor.

$\frac{(z + 5) (z - 5)}{3 (z - 5)}$

Step 2.2.2

Rewrite the expression.

$\frac{z + 5}{3}$