Question

\(\dfrac{a+b+2\sqrt{ab}}{\sqrt{a}+\sqrt{b}}-\dfrac{a-b}{\sqrt{a}-\sqrt{b}}\)

Answer 1

\(\dfrac{a+b+2\sqrt{ab}}{\sqrt{a}+\sqrt{b}}-\dfrac{a-b}{\sqrt{a}-\sqrt{b}}\\ =\dfrac{\left(\sqrt{a}+\sqrt{b}\right)^2}{\sqrt{a}+\sqrt{b}}-\dfrac{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{a}-\sqrt{b}}\\ =\sqrt{a}+\sqrt{b}-\sqrt{a}-\sqrt{b}\\ =0\)

Answer 2

\(\dfrac{a+2\sqrt{ab}+b}{\sqrt{a}+\sqrt{b}}-\dfrac{a-b}{\sqrt{a}-\sqrt{b}}\)

\(=\sqrt{a}+\sqrt{b}-\sqrt{a}-\sqrt{b}\)

=0