Question

Rút gọn 

\(\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2}+\sqrt{3}}+\frac{2-\sqrt{3}}{\sqrt{2}+\sqrt{2}-\sqrt{3}}\)

Answer 1

\(\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2}+\sqrt{3}}+\frac{2-\sqrt{3}}{\sqrt{2}+\sqrt{2}-\sqrt{3}}\)

= \(\frac{2+\sqrt{3}}{2\sqrt{2}+\sqrt{3}}+\frac{2-\sqrt{3}}{2\sqrt{2}-\sqrt{3}}\)

= \(\frac{\left(2+\sqrt{3}\right)\left(2\sqrt{2}-\sqrt{3}\right)+\left(2-\sqrt{3}\right)\left(2\sqrt{2}+\sqrt{3}\right)}{\left(2\sqrt{2}+\sqrt{3}\right)\left(2\sqrt{2}-\sqrt{3}\right)}\)

= \(\frac{4\sqrt{2}-2\sqrt{3}+2\sqrt{6}-3+4\sqrt{2}+2\sqrt{3}-2\sqrt{6}-3}{\left(2\sqrt{2}\right)^2-\left(\sqrt{3}\right)^2}\)

= \(\frac{8\sqrt{2}-6}{-5}\)

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