Trigonometry Examples

$\frac{1}{1 - \sqrt[3]{x^{2}}}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x^{2}}$ as $x^{\frac{2}{3}}$ .

$\frac{1}{1 - x^{\frac{2}{3}}}$

Step 2

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

$\frac{1}{1^{2} - x^{\frac{2}{3}}}$

Step 3

Rewrite $x^{\frac{2}{3}}$ as ${(x^{\frac{1}{3}})}^{2}$ .

$\frac{1}{1^{2} - {(x^{\frac{1}{3}})}^{2}}$

Step 4

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 $b = x^{\frac{1}{3}}$ .

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