Question

\(\dfrac{a\sqrt{a}-b\sqrt{b}}{\sqrt{a}-\sqrt{b}}\)

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Answer 1

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

Answer 2

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

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