Question

rationalize the denominator 3+√3/4-√3

Answer 1

multiply the top and bottom by the conjugate of the denominator, which is 4+sqrt3
\[\frac{3+\sqrt{3}}{4-\sqrt{3}}*\frac{4+\sqrt{3}}{4+\sqrt{3}}=\frac{15+7\sqrt{3}}{13}\]
(some "foiling" omitted)

Answer 2

it is right but where did you get the 13 from??

Answer 3

ok, that was part of the omitted foiling, which I'll now show.

in the bottom we have
\[(4-\sqrt{3})(4+\sqrt{3})=16+4\sqrt{3}-4\sqrt{3}-3=16-3=13\]

Answer 4

on the roots cancelled out ...alrighty