Đáp án:
a) \(\dfrac{{1 + x\sqrt x }}{{2x - \sqrt x + 1}}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)DK:x \ge 0;x \ne 1\\
A = \dfrac{{\left( {\sqrt x + 1} \right)\left( {x - \sqrt x + 1} \right)}}{{\left( {1 - \sqrt x } \right)\left( {\sqrt x + 1} \right)}}:\left[ {\dfrac{{{{\left( {1 - \sqrt x } \right)}^2} + \sqrt x \left( {\sqrt x + 1} \right)}}{{\left( {1 - \sqrt x } \right)\left( {\sqrt x + 1} \right)}}} \right]\\
= \dfrac{{\left( {\sqrt x + 1} \right)\left( {x - \sqrt x + 1} \right)}}{{\left( {1 - \sqrt x } \right)\left( {\sqrt x + 1} \right)}}.\dfrac{{\left( {1 - \sqrt x } \right)\left( {\sqrt x + 1} \right)}}{{1 - 2\sqrt x + x + x + \sqrt x }}\\
= \dfrac{{1 + x\sqrt x }}{{2x - \sqrt x + 1}}\\
b)A = 3\\
\to \dfrac{{1 + x\sqrt x }}{{2x - \sqrt x + 1}} = 3\\
\to 1 + x\sqrt x = 6x - 3\sqrt x + 3\\
\to x\sqrt x - 6x + 3\sqrt x - 2 = 0\\
\to \sqrt x = 5,522333393\\
\to x = 30,4961661
\end{array}\)
