To rationalize the given expression, we need to eliminate the radical from the denominator. To do that, we can multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of √5-√3 is √5+√3. Therefore, we have:
(2√3+√5) / (√5-√3) x (√5+√3) / (√5+√3)
Simplifying the numerator and the denominator using FOIL (First, Outer, Inner, Last) method, we get:
= [2√3(√5) + 2√3(√3) + √5(√5) + √5(√3)] / [(√5)(√5) - (√3)(√5) + (√5)(√3) - (√3)(√3)]
= [2√15 + 6 + 5 + √15] / [5 - 3 + √15 - 3]
= [3√15 + 11] / 2
Therefore, the answer is (3√15 + 11) / 2.