Rút gọn biểu thức: B=3√x−6/x−2√x+√x−3/√x−1/2−√x (với x>0,x≠4).

Với \(x > 0,\,x \ne 4\) ta có:

\(B = \frac{{3\sqrt x - 6}}{{x - 2\sqrt x }} + \frac{{\sqrt x - 3}}{{\sqrt x }} - \frac{1}{{2 - \sqrt x }}\)

\( = \frac{{3\left( {\sqrt x - 2} \right)}}{{\sqrt x \left( {\sqrt x - 2} \right)}} + \frac{{\sqrt x - 3}}{{\sqrt x }} + \frac{1}{{\sqrt x - 2}}\)\( = \frac{3}{{\sqrt x }} + \frac{{\sqrt x - 3}}{{\sqrt x }} + \frac{1}{{\sqrt x - 2}}\)

\( = \frac{{\sqrt x }}{{\sqrt x }} + \frac{1}{{\sqrt x - 2}}\) \( = 1 + \frac{1}{{\sqrt x - 2}}\)\( = \frac{{\sqrt x - 1}}{{\sqrt x - 2}}\) (với \(x > 0,\,x \ne 4\))