Basic Math Examples

$\frac{12 z - 4}{9 z^{2} - 1}$

Step 1

Factor $4$ out of $12 z - 4$ .

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Step 1.1

Factor $4$ out of $12 z$ .

$\frac{4 (3 z) - 4}{9 z^{2} - 1}$

Step 1.2

Factor $4$ out of $- 4$ .

$\frac{4 (3 z) + 4 (- 1)}{9 z^{2} - 1}$

Step 1.3

Factor $4$ out of $4 (3 z) + 4 (- 1)$ .

$\frac{4 (3 z - 1)}{9 z^{2} - 1}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{4 (3 z - 1)}{{(3 z)}^{2} - 1}$

Step 2.2

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

$\frac{4 (3 z - 1)}{{(3 z)}^{2} - 1^{2}}$

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 $a = 3 z$ and $b = 1$ .

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

Step 3

Cancel the common factor of $3 z - 1$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\frac{4}{3 z + 1}$