Question

Rút gọn

\(A=\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-3}-\frac{12}{3-\sqrt{6}}-\sqrt{6}\)

Answer 1

Lời giải:

\(A=\frac{15}{\sqrt{6}+1}-\frac{4}{3-\sqrt{6}}-\frac{12}{3-\sqrt{6}}-\sqrt{6}\)

\(=\frac{15}{\sqrt{6}+1}-\frac{16}{3-\sqrt{6}}-\sqrt{6}\)

\(=\frac{15(\sqrt{6}-1)}{(\sqrt{6}+1)(\sqrt{6}-1)}-\frac{16(3+\sqrt{6})}{(3-\sqrt{6})(3+\sqrt{6})}-\sqrt{6}\)

\(=\frac{15(\sqrt{6}-1)}{6-1}-\frac{16(3+\sqrt{6})}{3^2-6}-\sqrt{6}\)

\(=3(\sqrt{6}-1)-\frac{16}{3}(3+\sqrt{6})-\sqrt{6}\)

\(=\sqrt{6}(3-\frac{16}{3}-1)-(3+\frac{16}{3}.3)=\frac{-10\sqrt{6}}{3}+19\)