Trigonometry Examples

$\frac{h (x) (x - 1)}{x^{3} - 81 x}$

Step 1

Simplify the denominator.

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Step 1.1

Factor $x$ out of $x^{3} - 81 x$ .

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Step 1.1.1

Factor $x$ out of $x^{3}$ .

$\frac{h x (x - 1)}{x \cdot x^{2} - 81 x}$

Step 1.1.2

Factor $x$ out of $- 81 x$ .

$\frac{h x (x - 1)}{x \cdot x^{2} + x \cdot - 81}$

Step 1.1.3

Factor $x$ out of $x \cdot x^{2} + x \cdot - 81$ .

$\frac{h x (x - 1)}{x (x^{2} - 81)}$

Step 1.2

Rewrite $81$ as $9^{2}$ .

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

Step 1.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 9$ .

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

Step 2

Cancel the common factor of $x$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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