# How do you simplify (4+sqrt2)/(3+2sqrt3)?

Apr 15, 2018

Answer: $- 12 + 11 \sqrt{2} - 2 \sqrt{6}$
You rationalize it by multiply both numerator and denominator with its conjugate, which is: $3 - \sqrt{2}$
$\frac{4 + \sqrt{2}}{3 + \sqrt{2}} \left(\frac{3 + \sqrt{2}}{3 + \sqrt{2}}\right)$
=(12+3sqrt(2)-8sqrt(2)-2sqrt(2)sqrt(3))/(3^2-4(3)
$= - \frac{12 - 5 \sqrt{2} - 2 \sqrt{6}}{3}$