a)
\( \displaystyle\eqalign{
& {{{x^2} - 5} \over {x + \sqrt 5 }} = {{{x^2} - {{\left( {\sqrt 5 } \right)}^2}} \over {x + \sqrt 5 }} \cr
& = {{\left( {x - \sqrt 5 } \right)\left( {x + \sqrt 5 } \right)} \over {x + \sqrt 5 }} = x - \sqrt 5 \cr} \)
(với \(x \ne - \sqrt 5 \)).
b) \( \displaystyle{{{x^2} + 2\sqrt 2 x + 2} \over {{x^2} - 2}}\)
\( \displaystyle ={{{x^2} + 2\sqrt 2 x + 2} \over {{x^2} - 2}} \)\(\displaystyle = {{{x^2} + 2.x.\sqrt 2 + {{\left( {\sqrt 2 } \right)}^2}} \over {\left( {x + \sqrt 2 } \right)\left( {x - \sqrt 2 } \right)}} \)
\( = \dfrac{{{{\left( {x + \sqrt 2 } \right)}^2}}}{{\left( {x - \sqrt 2 } \right)\left( {x + \sqrt 2 } \right)}}\)
\(\displaystyle = {{x + \sqrt 2 } \over {x - \sqrt 2 }} \)
(với \(x \ne \pm \sqrt 2 \) ).
