# How do you add (3sqrt3 + 9sqrt3 + sqrt6 + 3sqrt9) /(sqrt4 - 9sqrt9)?

Apr 13, 2015

The first thing you may notice, is that the numerator is easy to simplify:

$\text{numerator} = \sqrt{4} - 9 \sqrt{9} = 2 - 9 \cdot 3 = - 25$

We will forget that for a while and focus on the denominator:

Add like roots and simplify $\sqrt{9} = 3$

$\text{denominator} = \left(3 + 9\right) \sqrt{3} + \sqrt{6} + 3 \cdot 3$

Since you can't simplify this any further:

$\text{answer} = - \frac{12 \sqrt{3} + \sqrt{6} + 9}{25}$