Trigonometry Examples

$\frac{x^{2}}{\sqrt{10} - \sqrt{5}}$

Step 1

Multiply $\frac{x^{2}}{\sqrt{10} - \sqrt{5}}$ by $\frac{\sqrt{10} + \sqrt{5}}{\sqrt{10} + \sqrt{5}}$ .

$\frac{x^{2}}{\sqrt{10} - \sqrt{5}} \cdot \frac{\sqrt{10} + \sqrt{5}}{\sqrt{10} + \sqrt{5}}$

Step 2

Multiply $\frac{x^{2}}{\sqrt{10} - \sqrt{5}}$ by $\frac{\sqrt{10} + \sqrt{5}}{\sqrt{10} + \sqrt{5}}$ .

$\frac{x^{2} (\sqrt{10} + \sqrt{5})}{(\sqrt{10} - \sqrt{5}) (\sqrt{10} + \sqrt{5})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{x^{2} (\sqrt{10} + \sqrt{5})}{{\sqrt{10}}^{2} + \sqrt{50} - \sqrt{50} - {\sqrt{5}}^{2}}$

Step 4

Simplify.

$\frac{x^{2} (\sqrt{10} + \sqrt{5})}{5}$