Trigonometry Examples

$\frac{x + 2}{y - \sqrt{2}}$

Step 1

Multiply $\frac{x + 2}{y - \sqrt{2}}$ by $\frac{y + \sqrt{2}}{y + \sqrt{2}}$ .

$\frac{x + 2}{y - \sqrt{2}} \cdot \frac{y + \sqrt{2}}{y + \sqrt{2}}$

Step 2

Multiply $\frac{x + 2}{y - \sqrt{2}}$ by $\frac{y + \sqrt{2}}{y + \sqrt{2}}$ .

$\frac{(x + 2) (y + \sqrt{2})}{(y - \sqrt{2}) (y + \sqrt{2})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{(x + 2) (y + \sqrt{2})}{y^{2} + y \sqrt{2} - \sqrt{2} y - {\sqrt{2}}^{2}}$

Step 4

Simplify.

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Step 4.1

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

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Step 4.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$\frac{(x + 2) (y + \sqrt{2})}{y^{2} - {(2^{\frac{1}{2}})}^{2}}$

Step 4.1.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{(x + 2) (y + \sqrt{2})}{y^{2} - 2^{\frac{1}{2} \cdot 2}}$

Step 4.1.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{(x + 2) (y + \sqrt{2})}{y^{2} - 2^{\frac{2}{2}}}$

Step 4.1.4

Cancel the common factor of $2$ .

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Step 4.1.4.1

Cancel the common factor.

$\frac{(x + 2) (y + \sqrt{2})}{y^{2} - 2^{\frac{2}{2}}}$

Step 4.1.4.2

Rewrite the expression.

$\frac{(x + 2) (y + \sqrt{2})}{y^{2} - 2^{1}}$

Step 4.1.5

Evaluate the exponent.

$\frac{(x + 2) (y + \sqrt{2})}{y^{2} - 1 \cdot 2}$

Step 4.2

Multiply $- 1$ by $2$ .

$\frac{(x + 2) (y + \sqrt{2})}{y^{2} - 2}$