Question

\frac{a+\sqrt{ab}}{\sqrt{a}+\sqrt{b}}

 

Answer 1

`(a+sqrt{ab})/(sqrta+sqrtb)`

`=(sqrta.sqrta+sqrta.sqrtb)/(sqrta+sqrtb)`

`=(sqrta(sqrta+sqrtb))/(sqrta+sqrtb)`

`=sqrta`

Answer 2

\(\dfrac{a+\sqrt{ab}}{\sqrt{a}+\sqrt{b}}\)

\(=\dfrac{\sqrt{a}\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{a}+\sqrt{b}}\)

\(=\sqrt{a}\)