Question 85653
Multiply the numerator and denominator by the conjugate of {{{3sqrt(5) + 4sqrt(3)}}}, which is {{{3sqrt(5) - 4sqrt(3)}}}:

{{{(sqrt(5) - sqrt(3))/(3sqrt(5) + 4sqrt(3))}}} * {{{(3sqrt(4) - 4sqrt(3))/(3sqrt(5) - 4sqrt(3))}}}

Now, do FOIL for the tops and the bottoms become the difference of the squares:

{{{(3sqrt(20) - 4sqrt(15) - 3sqrt(12) - 4(3))/(9(5) - 16(3))}}} =

{{{(6sqrt(5) - 4sqrt(15) - 6sqrt(3) - 12)/(-3)}}} =

{{{(-6sqrt(5) + 4sqrt(15) + 6sqrt(3) + 12)/3}}}