Rationalize the denominator and simplify if possible. √5+√3 / √5-√3

Answer 1

multiply top and bottom by the conjugate, and recall that (a-b)(a+b) = a^2-b^2

(√5+√3)/(√5-√3) * (√5+√3)/(√5+√3) = (√5+√3)^2/(5-3) = (8+2√15)/2 = 4+√15