Question

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

Answer 1

`6/(sqrt11+sqrt5)-(11+sqrt11)/(sqrt11+1)+1/(2sqrt5)`

`=(6(sqrt11-sqrt5))/(11-5)-(sqrt11(sqrt11+1))/(sqrt11+1)+sqrt5/10`

`=sqrt11-sqrt5-sqrt11+sqrt5/10`

`=sqrt5/10-sqrt5=(-9sqrt5)/10`

Answer 2

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

\(=\sqrt{11}-\sqrt{5}-\sqrt{11}+\dfrac{1}{10}\sqrt{5}\)

\(=-\dfrac{9}{10}\sqrt{5}\)