Rút gọn: a) A =( x - 2 √x + 1 / √x - 1) + (x √x + 1 / x - √x + 1) + 1 với x ≥ 0, x khác 1 b) B =[( x + 3 / x - 9) + ( 1 / √3 )] : √x / √x - 3 với x > 0 , x khác 9

\[\begin{array}{l} a)\,\,\,A = \frac{{x - 2\sqrt x + 1}}{{\sqrt x - 1}} + \frac{{x\sqrt x + 1}}{{x - \sqrt x + 1}} + 1\,\,\,\left( {x \ge 0,\,\,x \ne 1} \right)\\ = \frac{{{{\left( {\sqrt x - 1} \right)}^2}}}{{\sqrt x - 1}} + \frac{{\left( {\sqrt x + 1} \right)\left( {x - \sqrt x + 1} \right)}}{{x - \sqrt x + 1}}\\ = \sqrt x - 1 + \sqrt x + 1 + 1\\ = 2\sqrt x + 1.\\ b)\,\,\,B = \left[ {\frac{{x + 3}}{{x - 9}} - \frac{1}{{\sqrt 3 }}} \right]:\frac{{\sqrt x }}{{\sqrt x - 3}}\,\,\,\,\,\left( {x > 0,\,\,\,x \ne 9} \right)\\ = \frac{{\sqrt 3 x + 3\sqrt 3 - x + 9}}{{\sqrt 3 \left( {\sqrt x - 3} \right)\left( {\sqrt x + 3} \right)}}.\frac{{\sqrt x - 3}}{{\sqrt x }}\\ = \frac{{\left( {\sqrt 3 - 1} \right)x + 3\sqrt 3 + 9}}{{\sqrt 3 \left( {\sqrt x + 3} \right)\sqrt x }}. \end{array}\]