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