# How do you rationalize the denominator and simplify (4-2sqrt5)/(6-5sqrt5)?

Mar 27, 2016

$\frac{26 - 8 \sqrt{5}}{89}$

#### Explanation:

Multiply the numerator and the denominator by the conjugate $6 + 5 \sqrt{5}$ of the denominator.

Use $\left(a - b\right) \left(a + b\right) = \left({a}^{2} - {b}^{2}\right)$ to simplify the denominator.

Expand the product in the numerator.

The ratio simplifies to $\frac{26 - 8 \sqrt{5}}{89}$