Question

\(\dfrac{\sqrt{a}+a\sqrt{b}-\sqrt{b}-b\sqrt{a}}{ab-1}\)

Answer 1

\(=\dfrac{\sqrt{a}\left(1+\sqrt{ab}\right)-\sqrt{b}\left(1+\sqrt{ab}\right)}{ab-1}=\dfrac{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{ab}+1\right)}{\left(\sqrt{ab}+1\right)\left(\sqrt{ab}-1\right)}=\dfrac{\sqrt{a}-\sqrt{b}}{\sqrt{ab}-1}\)

Answer 2

`= (sqrt a(1 + sqrt(ab)) - sqrt b(1 + sqrt ab))/(sqrt(ab) - 1)(sqrt(ab) +1))`

`= ((sqrt a - sqrt b)(1 + sqrt (ab))/((sqrt (ab) - 1)(sqrt (ab) +1))`

`= (sqrt a - sqrt b)/(sqrt (ab) - 1)`