Ta có:\(\dfrac{30}{\sqrt{6}+1}+\dfrac{2}{\sqrt{6}-2}+\dfrac{6}{3-\sqrt{6}}\)
=\(\dfrac{30\cdot\left(\sqrt{6}-1\right)}{\left(\sqrt{6}+1\right)\cdot\left(\sqrt{6}-1\right)}+\dfrac{2\cdot\left(\sqrt{6}+2\right)}{\left(\sqrt{6}-2\right)\cdot\left(\sqrt{6}+2\right)}+\dfrac{6\cdot\left(3+\sqrt{6}\right)}{\left(3-\sqrt{6}\right)\cdot\left(3+\sqrt{6}\right)}\)
=\(\dfrac{30\cdot\left(\sqrt{6}-1\right)}{\sqrt{6}^2-1^2}+\dfrac{2\cdot\left(\sqrt{6}+2\right)}{\sqrt{6}^2-2^2}+\dfrac{6\cdot\left(3+\sqrt{6}\right)}{3^2-\sqrt{6}^2}\)
=\(\dfrac{30\cdot\left(\sqrt{6}-1\right)}{5}+\dfrac{2\cdot\left(\sqrt{6}+2\right)}{2}+\dfrac{6\cdot\left(3+\sqrt{6}\right)}{3}\)
= \(6\cdot\left(\sqrt{6}-1\right)+\left(\sqrt{6}+2\right)+2\cdot\left(3+\sqrt{6}\right)\)
= \(6\sqrt{6}-6+\sqrt{6}+2+6+2\sqrt{6}\)
=\(\left(6\sqrt{6}+\sqrt{6}+2\sqrt{6}\right)+\left(-6+2+6\right)\)
= \(9\sqrt{6}+2\)
Ta có:
\(\dfrac{30}{\sqrt{6}+1}+\dfrac{2}{\sqrt{6}-2}+\dfrac{6}{3-\sqrt{6}}\)
= \(\dfrac{30\left(\sqrt{6}-1\right)}{6-1}+\dfrac{2\left(\sqrt{6}+2\right)}{6-4}-\dfrac{6\left(3+\sqrt{6}\right)}{9-6}\)
= \(6\left(\sqrt{6}-1\right)+\left(\sqrt{6}+2\right)-2\left(3+\sqrt{6}\right)\)
= \(6\sqrt{6}-6+\sqrt{6}+2-6-2\sqrt{6}\)
= \(5\sqrt{6}-10\)
= \(5\left(\sqrt{6}-2\right)\)
