Finite Math Examples

$\frac{15 + 30}{5 - \frac{20}{x^{2}}}$

Step 1

Add $15$ and $30$ .

$\frac{45}{5 - \frac{20}{x^{2}}}$

Step 2

Factor $5$ out of $5 - \frac{20}{x^{2}}$ .

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Step 2.1

Factor $5$ out of $5$ .

$\frac{45}{5 (1) - \frac{20}{x^{2}}}$

Step 2.2

Factor $5$ out of $- \frac{20}{x^{2}}$ .

$\frac{45}{5 (1) + 5 (- \frac{4}{x^{2}})}$

Step 2.3

Factor $5$ out of $5 (1) + 5 (- \frac{4}{x^{2}})$ .

$\frac{45}{5 (1 - \frac{4}{x^{2}})}$

Step 3

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

$\frac{45}{5 (1^{2} - \frac{4}{x^{2}})}$

Step 4

Rewrite $\frac{4}{x^{2}}$ as ${(\frac{2}{x})}^{2}$ .

$\frac{45}{5 (1^{2} - {(\frac{2}{x})}^{2})}$

Step 5

Factor.

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Step 5.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = \frac{2}{x}$ .

$\frac{45}{5 ((1 + \frac{2}{x}) (1 - \frac{2}{x}))}$

Step 5.2

Remove unnecessary parentheses.

$\frac{45}{5 (1 + \frac{2}{x}) (1 - \frac{2}{x})}$

Step 6

Reduce the expression $\frac{45}{5 (1 + \frac{2}{x}) (1 - \frac{2}{x})}$ by cancelling the common factors.

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Step 6.1

Factor $5$ out of $45$ .

$\frac{5 \cdot 9}{5 (1 + \frac{2}{x}) (1 - \frac{2}{x})}$

Step 6.2

Factor $5$ out of $5 (1 + \frac{2}{x}) (1 - \frac{2}{x})$ .

$\frac{5 \cdot 9}{5 ((1 + \frac{2}{x}) (1 - \frac{2}{x}))}$

Step 6.3

Cancel the common factor.

$\frac{5 \cdot 9}{5 ((1 + \frac{2}{x}) (1 - \frac{2}{x}))}$

Step 6.4

Rewrite the expression.

$\frac{9}{(1 + \frac{2}{x}) (1 - \frac{2}{x})}$