Basic Math Examples

$\frac{z^{2} - 1}{z^{2 - 4 z - 5}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $1$ as $1^{2}$ .

$\frac{z^{2} - 1^{2}}{z^{2 - 4 z - 5}}$

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 $b = 1$ .

$\frac{(z + 1) (z - 1)}{z^{2 - 4 z - 5}}$

Step 2

Subtract $5$ from $2$ .

$\frac{(z + 1) (z - 1)}{z^{- 4 z - 3}}$