a) Với \(x \ge 0,y \ge 0\) và \(x \ne y,\) ta có:
\(\displaystyle {{x\sqrt x - y\sqrt y } \over {\sqrt x - \sqrt y }} = {{\sqrt {{x^3}} - \sqrt {{y^3}} } \over {\sqrt x - \sqrt y }} \)\( \displaystyle = {{(\sqrt x - \sqrt y )(x + \sqrt {xy} + y)} \over {\sqrt x - \sqrt y }} \)
\( = x + \sqrt {xy} + y\)
b) Với \(x \ge 0,\) ta có:
\(\eqalign{
& {{x - \sqrt {3x} + 3} \over {x\sqrt x + 3\sqrt 3 }} = {{x - \sqrt {3x} + 3} \over {\sqrt {{x^3}} + \sqrt {{3^3}} }} \cr
& = {{x - \sqrt {3x} + 3} \over {(\sqrt x + \sqrt 3 )(x - \sqrt {3x} + 3)}}\cr
& = {1 \over {\sqrt x + \sqrt 3 }}\cr} \)
