Chứng minh rằng B = căn x/ ( căn x − 2) .

c) Với \(x \ge 0,\,\,x \ne 4,\) ta có:

\(B = \frac{x}{{x - 4}} - \frac{1}{{2 - \sqrt x }} + \frac{1}{{\sqrt x + 2}}\)

 \( = \frac{x}{{\left( {\sqrt x + 2} \right)\left( {\sqrt x - 2} \right)}} + \frac{{\sqrt x + 2}}{{\left( {\sqrt x + 2} \right)\left( {\sqrt x - 2} \right)}} + \frac{{\sqrt x - 2}}{{\left( {\sqrt x + 2} \right)\left( {\sqrt x - 2} \right)}}\)

 \( = \frac{{x + \sqrt x + 2 + \sqrt x - 2}}{{\left( {\sqrt x + 2} \right)\left( {\sqrt x - 2} \right)}}\)\( = \frac{{x + 2\sqrt x }}{{\left( {\sqrt x + 2} \right)\left( {\sqrt x - 2} \right)}}\)

 \( = \frac{{\sqrt x \left( {\sqrt x + 2} \right)}}{{\left( {\sqrt x + 2} \right)\left( {\sqrt x - 2} \right)}} = \frac{{\sqrt x }}{{\sqrt x - 2}}.\)

Vậy với \(x \ge 0,\,\,x \ne 4,\) thì \(B = \frac{{\sqrt x }}{{\sqrt x - 2}}.\)