# How do you rationalize the denominator (2+sqrt3)/(5-sqrt3)?

Apr 1, 2015

 (2 + sqrt(3))/(5 - sqrt(3)) = ((2 + sqrt(3))xx(5 + sqrt(3)))/((5 - sqrt(3))xx(5 + sqrt(3))

$= \frac{10 + 5 \sqrt{3} + 2 \sqrt{3} + {\left(\sqrt{3}\right)}^{2}}{25 - {\left(\sqrt{3}\right)}^{2}}$

$= \frac{10 + 3 + 8 \sqrt{3}}{25 - 3}$

$= \frac{13 + 8 \sqrt{3}}{22}$