Basic Math Examples

$\frac{z^{2} - 1}{36 z + 36} \div \frac{z - 1}{6}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{z^{2} - 1}{36 z + 36} \cdot \frac{6}{z - 1}$

Step 2

Simplify the numerator.

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Step 2.1

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

$\frac{z^{2} - 1^{2}}{36 z + 36} \cdot \frac{6}{z - 1}$

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 $b = 1$ .

$\frac{(z + 1) (z - 1)}{36 z + 36} \cdot \frac{6}{z - 1}$

Step 3

Simplify terms.

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Step 3.1

Factor $36$ out of $36 z + 36$ .

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Step 3.1.1

Factor $36$ out of $36 z$ .

$\frac{(z + 1) (z - 1)}{36 (z) + 36} \cdot \frac{6}{z - 1}$

Step 3.1.2

Factor $36$ out of $36$ .

$\frac{(z + 1) (z - 1)}{36 (z) + 36 (1)} \cdot \frac{6}{z - 1}$

Step 3.1.3

Factor $36$ out of $36 (z) + 36 (1)$ .

$\frac{(z + 1) (z - 1)}{36 (z + 1)} \cdot \frac{6}{z - 1}$

Step 3.2

Cancel the common factor of $z - 1$ .

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Step 3.2.1

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

$\frac{(z - 1) (z + 1)}{36 (z + 1)} \cdot \frac{6}{z - 1}$

Step 3.2.2

Cancel the common factor.

$\frac{(z - 1) (z + 1)}{36 (z + 1)} \cdot \frac{6}{z - 1}$

Step 3.2.3

Rewrite the expression.

$\frac{z + 1}{36 (z + 1)} \cdot 6$

Step 3.3

Cancel the common factor of $6$ .

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Step 3.3.1

Factor $6$ out of $36 (z + 1)$ .

$\frac{z + 1}{6 (6 (z + 1))} \cdot 6$

Step 3.3.2

Cancel the common factor.

$\frac{z + 1}{6 (6 (z + 1))} \cdot 6$

Step 3.3.3

Rewrite the expression.

$\frac{z + 1}{6 (z + 1)}$

Step 3.4

Cancel the common factor of $z + 1$ .

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Step 3.4.1

Cancel the common factor.

$\frac{z + 1}{6 (z + 1)}$

Step 3.4.2

Rewrite the expression.

$\frac{1}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{6}$

Decimal Form:

$0.1\overline{6}$