Question

How do you simplify `9/(sqrt6 - sqrt5)`?

Answer 1

This problem can be solved by using using the conjugate of the denominator and rationalization

Explanation:

`\frac{9}{\sqrt{6}-\sqrt{5}}`

`=frac{9}{\sqrt{6}-\sqrt{5}} * frac{\sqrt{6}+\sqrt{5}}{\sqrt{6}+\sqrt{5}}`

`=frac{9*(\sqrt{6}+\sqrt{5})}{(\sqrt{6})^2-(\sqrt{5})^2}`

`=frac{9*(\sqrt{6}+\sqrt{5})}{6-5}=9*(\sqrt{6}+\sqrt{5})`