Question

Simplify the following: 2/ root 5 + root 3 + 1/ root 3 + root 2 - 3/ root 5 + root 2

Answer 1

Dear student
$$\begin{gathered} Wehave, \\ \frac{2}{\sqrt{5}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{2}}-\frac{3}{\sqrt{5}+\sqrt{2}} \\ =\frac{2}{\sqrt{5}+\sqrt{3}}\times \frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}-\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{2}}\times \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}-\frac{3}{\sqrt{5}+\sqrt{2}}\times \frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}-\sqrt{2}} \\ =\frac{2\sqrt{5}-2\sqrt{3}}{5-3}+\frac{\sqrt{3}-\sqrt{2}}{3-2}-\frac{3\sqrt{5}-3\sqrt{2}}{5-2} \\ =\frac{2\sqrt{5}-2\sqrt{3}}{2}+\frac{\sqrt{3}-\sqrt{2}}{1}-\frac{3\sqrt{5}-3\sqrt{2}}{3} \\ =\frac{6\sqrt{5}-6\sqrt{3}+6\sqrt{3}-6\sqrt{2}-6\sqrt{5}+6\sqrt{2}}{6} \\ =0 \end{gathered}$$
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