Basic Math Examples

$\frac{z^{2}}{z^{2} - 1} - \frac{3 z + 2}{z^{2} - 1}$

Step 1

Simplify terms.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{z^{2} - (3 z + 2)}{z^{2} - 1}$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$\frac{z^{2} - (3 z) - 1 \cdot 2}{z^{2} - 1}$

Step 1.2.2

Multiply $3$ by $- 1$ .

$\frac{z^{2} - 3 z - 1 \cdot 2}{z^{2} - 1}$

Step 1.2.3

Multiply $- 1$ by $2$ .

$\frac{z^{2} - 3 z - 2}{z^{2} - 1}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{z^{2} - 3 z - 2}{z^{2} - 1^{2}}$

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 $b = 1$ .

$\frac{z^{2} - 3 z - 2}{(z + 1) (z - 1)}$