Question

\(\dfrac{a-b}{\sqrt{a}-\sqrt{b}}\) - \(\dfrac{\sqrt{a^3}-\sqrt{b^3}}{a-b}\)

Answer 1

\(\dfrac{a-b}{\sqrt{a}-\sqrt{b}}-\dfrac{\sqrt{a^3}-\sqrt{b^3}}{a-b}\)

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

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

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

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

Answer 2

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