The hard part of this one is reading the question. I'm going to assume those root 5s are in the numerators.
[tex]\frac 3 4 \sqrt{5} - \sqrt{3} + \frac 2 4 \sqrt{5} + \sqrt{3} = A \sqrt{5} + B\sqrt{3}[/tex]
Two fourths? Really? OK.
[tex]\frac 3 4 \sqrt{5} - \sqrt{3} + \frac 2 4 \sqrt{5} + \sqrt{3}[/tex]
[tex]=(\frac 3 4 + \frac 2 4)\sqrt{5} + (-1 + 1)\sqrt{3}[/tex]
[tex]=\frac 5 4 \sqrt{5}[/tex]
Answer: A=5/4, B=0
