Rút gọn biểu thức A=x+√x/x−1−√x/x(√x−1) với x>0;x≠1.

\[A = \frac{{\sqrt x (\sqrt x + 1)}}{{(\sqrt x - 1)(\sqrt x + 1)}} - \frac{1}{{\sqrt x (\sqrt x - 1)}}\]

\[ = \frac{{\sqrt x }}{{\sqrt x - 1}} - \frac{1}{{\sqrt x (\sqrt x - 1)}}\]

\[{\rm{ }} = \frac{{x - 1}}{{\sqrt x (\sqrt x - 1)}}{\rm{ = }}\frac{{(\sqrt x - 1)(\sqrt x + 1)}}{{\sqrt x (\sqrt x - 1)}} = \frac{{\sqrt x + 1}}{{\sqrt x }}\]