Ta có \(\dfrac{{a - b}}{{\sqrt a - \sqrt b }} - \dfrac{{\sqrt {{a^3}} + \sqrt {{b^3}} }}{{a - b}}\)$ = \dfrac{{a - b}}{{\sqrt a - \sqrt b }} - \dfrac{{\left( {\sqrt a + \sqrt b } \right)\left[ {{{\left( {\sqrt a } \right)}^2} - \sqrt a .\sqrt b + {{\left( {\sqrt b } \right)}^2}} \right]}}{{{{\left( {\sqrt a } \right)}^2} - {{\left( {\sqrt b } \right)}^2}}}$

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