Question

Rút gọn BT :

A=\(\frac{3}{2+\sqrt{3}}+\frac{13}{4-\sqrt{3}}+\frac{6}{\sqrt{3}}\)

Answer 1

\(A=\frac{3}{2+\sqrt{3}}+\frac{13}{4-\sqrt{3}}+\frac{6}{\sqrt{3}}\)

\(=\frac{3\left(2-\sqrt{3}\right)}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}+\frac{13\left(4+\sqrt{3}\right)}{\left(4-\sqrt{3}\right)\left(4+\sqrt{3}\right)}+\frac{6}{\sqrt{3}}\)

\(=6-3\sqrt{3}+4+\sqrt{3}+\frac{6}{\sqrt{3}}\)

\(=10-2\sqrt{3}+\frac{6}{\sqrt{3}}\)

\(=\frac{10\sqrt{3}-6+6\sqrt{3}}{\sqrt{3}}\)

\(=\frac{16\sqrt{3}-6}{\sqrt{3}}\)