Exercise
Simplify the expression:
\frac{\sqrt{5}}{2\sqrt{3}-1}-\frac{\sqrt{3}}{2\sqrt{5}+3}
Final Answer
Solution
Using Powers and Roots rules we get:
\frac{\sqrt{5}}{2\sqrt{3}-1}-\frac{\sqrt{3}}{2\sqrt{5}+3}=
=\frac{\sqrt{5}(2\sqrt{3}+1)}{(2\sqrt{3}-1)(2\sqrt{3}+1)}-\frac{\sqrt{3}(2\sqrt{5}-3)}{(2\sqrt{5}+3)(2\sqrt{5}-3)}=
=\frac{\sqrt{5}(2\sqrt{3}+1)}{12-1}-\frac{\sqrt{3}(2\sqrt{5}-3)}{20-9}=
=\frac{1}{11}\cdot\sqrt{5}(2\sqrt{3}+1)-\frac{1}{11}\cdot\sqrt{3}(2\sqrt{5}-3)=
=\frac{1}{11}(2\sqrt{15}+\sqrt{5})-\frac{1}{11}(2\sqrt{15}-3\sqrt{3})=
=\frac{1}{11}(2\sqrt{15}+\sqrt{5}-2\sqrt{15}+3\sqrt{3})=
=\frac{1}{11}(\sqrt{5}+3\sqrt{3})