Question

\(\dfrac{5}{\sqrt{11}-\sqrt{6}}-\dfrac{2}{\sqrt{6}-2}+\dfrac{11-\sqrt{11}}{1-\sqrt{11}}\)

thực hiện phép tính

giúp tuui nha

Answer 1

\(=\dfrac{5.\left(\sqrt{11}+\sqrt{6}\right)}{5}-\dfrac{2.\left(\sqrt{6}+2\right)}{2}+\dfrac{\sqrt{11}.\left(\sqrt{11}-1\right)}{1-\sqrt{11}}\)

= \(\sqrt{11}+\sqrt{6}-\sqrt{6}-2-\sqrt{11}\)

= -2

Answer 2

\(=\dfrac{5\left(\sqrt{11}+\sqrt{6}\right)}{\left(\sqrt{11}-\sqrt{6}\right)\left(\sqrt{11}+\sqrt{6}\right)}-\dfrac{2\left(\sqrt{6}+2\right)}{\left(\sqrt{6}-2\right)\left(\sqrt{6}+2\right)}+\dfrac{\sqrt{11}\left(\sqrt{11}-1\right)}{\left(\sqrt{11}-1\right)}\)

\(=\dfrac{5\left(\sqrt{11}+\sqrt{6}\right)}{5}-\dfrac{2\left(\sqrt{6}+2\right)}{2}+\dfrac{\sqrt{11}\left(\sqrt{11}-1\right)}{\left(\sqrt{11}-1\right)}\)

\(=\left(\sqrt{11}+\sqrt{6}\right)-\left(\sqrt{6}+2\right)+\sqrt{11}\)

\(=2\sqrt{11}-2\)