Basic Math Examples

$\frac{w^{2} - 36}{25 w + 150} \div \frac{w - 6}{30}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{w^{2} - 36}{25 w + 150} \cdot \frac{30}{w - 6}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $36$ as $6^{2}$ .

$\frac{w^{2} - 6^{2}}{25 w + 150} \cdot \frac{30}{w - 6}$

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 $a = w$ and $b = 6$ .

$\frac{(w + 6) (w - 6)}{25 w + 150} \cdot \frac{30}{w - 6}$

Step 3

Simplify terms.

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Step 3.1

Factor $25$ out of $25 w + 150$ .

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Step 3.1.1

Factor $25$ out of $25 w$ .

$\frac{(w + 6) (w - 6)}{25 (w) + 150} \cdot \frac{30}{w - 6}$

Step 3.1.2

Factor $25$ out of $150$ .

$\frac{(w + 6) (w - 6)}{25 w + 25 \cdot 6} \cdot \frac{30}{w - 6}$

Step 3.1.3

Factor $25$ out of $25 w + 25 \cdot 6$ .

$\frac{(w + 6) (w - 6)}{25 (w + 6)} \cdot \frac{30}{w - 6}$

Step 3.2

Cancel the common factor of $w - 6$ .

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Step 3.2.1

Factor $w - 6$ out of $(w + 6) (w - 6)$ .

$\frac{(w - 6) (w + 6)}{25 (w + 6)} \cdot \frac{30}{w - 6}$

Step 3.2.2

Cancel the common factor.

$\frac{(w - 6) (w + 6)}{25 (w + 6)} \cdot \frac{30}{w - 6}$

Step 3.2.3

Rewrite the expression.

$\frac{w + 6}{25 (w + 6)} \cdot 30$

Step 3.3

Cancel the common factor of $5$ .

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Step 3.3.1

Factor $5$ out of $25 (w + 6)$ .

$\frac{w + 6}{5 (5 (w + 6))} \cdot 30$

Step 3.3.2

Factor $5$ out of $30$ .

$\frac{w + 6}{5 (5 (w + 6))} \cdot (5 (6))$

Step 3.3.3

Cancel the common factor.

$\frac{w + 6}{5 (5 (w + 6))} \cdot (5 \cdot 6)$

Step 3.3.4

Rewrite the expression.

$\frac{w + 6}{5 (w + 6)} \cdot 6$

Step 3.4

Combine $\frac{w + 6}{5 (w + 6)}$ and $6$ .

$\frac{(w + 6) \cdot 6}{5 (w + 6)}$

Step 3.5

Cancel the common factor of $w + 6$ .

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Step 3.5.1

Cancel the common factor.

$\frac{(w + 6) \cdot 6}{5 (w + 6)}$

Step 3.5.2

Rewrite the expression.

$\frac{6}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{6}{5}$

Decimal Form:

$1.2$

Mixed Number Form:

$1 \frac{1}{5}$