Basic Math Examples

$\frac{4 v - 24}{v^{2} - 36} \cdot (5 v + 30)$

Step 1

Factor $4$ out of $4 v - 24$ .

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Step 1.1

Factor $4$ out of $4 v$ .

$\frac{4 (v) - 24}{v^{2} - 36} \cdot (5 v + 30)$

Step 1.2

Factor $4$ out of $- 24$ .

$\frac{4 v + 4 \cdot - 6}{v^{2} - 36} \cdot (5 v + 30)$

Step 1.3

Factor $4$ out of $4 v + 4 \cdot - 6$ .

$\frac{4 (v - 6)}{v^{2} - 36} \cdot (5 v + 30)$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{4 (v - 6)}{v^{2} - 6^{2}} \cdot (5 v + 30)$

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 $a = v$ and $b = 6$ .

$\frac{4 (v - 6)}{(v + 6) (v - 6)} \cdot (5 v + 30)$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $v - 6$ .

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Step 3.1.1

Cancel the common factor.

$\frac{4 (v - 6)}{(v + 6) (v - 6)} \cdot (5 v + 30)$

Step 3.1.2

Rewrite the expression.

$\frac{4}{v + 6} \cdot (5 v + 30)$

Step 3.2

Multiply $\frac{4}{v + 6}$ by $5 v + 30$ .

$\frac{4 (5 v + 30)}{v + 6}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $5$ out of $5 v + 30$ .

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Step 4.1.1

Factor $5$ out of $5 v$ .

$\frac{4 (5 (v) + 30)}{v + 6}$

Step 4.1.2

Factor $5$ out of $30$ .

$\frac{4 (5 v + 5 \cdot 6)}{v + 6}$

Step 4.1.3

Factor $5$ out of $5 v + 5 \cdot 6$ .

$\frac{4 (5 (v + 6))}{v + 6}$

$\frac{4 \cdot 5 (v + 6)}{v + 6}$

Step 4.2

Multiply $4$ by $5$ .

$\frac{20 (v + 6)}{v + 6}$

Step 5

Cancel the common factor of $v + 6$ .

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Step 5.1

Cancel the common factor.

$\frac{20 (v + 6)}{v + 6}$

Step 5.2

Divide $20$ by $1$ .

$20$