# How do you rationalize the denominator and simplify 5/(sqrt14-2)?

May 9, 2018

$\setminus \frac{5 \setminus \sqrt{14} + 10}{10}$

#### Explanation:

Use the identity $\left(a - b\right) \left(a + b\right) = {a}^{2} - {b}^{2}$ in the following way:

$\setminus \frac{5}{\setminus \sqrt{14} - 2} = \setminus \frac{5}{\setminus \sqrt{14} - 2} \setminus \cdot 1 = \setminus \frac{5}{\left(\setminus \sqrt{14} - 2\right)} \setminus \cdot \setminus \frac{\left(\setminus \sqrt{14} + 2\right)}{\left(\setminus \sqrt{14} + 2\right)}$

Now, the numerator is simply $5 \left(\setminus \sqrt{14} + 2\right) = 5 \setminus \sqrt{14} + 10$, while at the denominator we have the forementioned identity:

$\left(\setminus \sqrt{14} - 2\right) \left(\setminus \sqrt{14} + 2\right) = {\left(\setminus \sqrt{14}\right)}^{2} - {2}^{2} = 14 - 4 = 10$