Question

rút gọn biểu thức :

\(A=\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6-2}}-\frac{12}{3-\sqrt{6}}\right)\)  \(\left(\sqrt{6}+11\right)\)

 

Answer 1

\(A=\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right)\) \(\left(\sqrt{6}+11\right)\)

\(A=\left(\frac{3.\left(\sqrt{6}+1\right)\left(\sqrt{6}-1\right)}{\sqrt{6}+1}\right)+\left(\frac{2.\left(\sqrt{6}+2\right)\left(\sqrt{6}-2\right)}{\sqrt{6}-2}\right)-\frac{4.\left(3-\sqrt{6}\right)\left(3+\sqrt{6}\right)}{3-\sqrt{6}}\)\(\left(\sqrt{6}+11\right)\)

\(A=\left(3.\left(\sqrt{6}-1\right)+2.\left(\sqrt{6}+2\right)-4.\left(3+\sqrt{6}\right)\right)\left(\sqrt{6}+11\right)\)

\(A=\left(\sqrt{6}-11\right)\left(\sqrt{6}+11\right)=-115\)