Đáp án:
\(\frac{{x\sqrt x + 1}}{{x - 1}} - \frac{{x - 1}}{{\sqrt x + 1}} = \frac{{\sqrt x }}{{\sqrt x - 1}}\)
Giải thích các bước giải:
\[\begin{array}{l}
\frac{{x\sqrt x + 1}}{{x - 1}} - \frac{{x - 1}}{{\sqrt x + 1}}\,\,\,\,\left( {DK:\,\,\,x \ge 0,\,\,\,x \ne 1} \right)\\
= \frac{{\left( {\sqrt x + 1} \right)\left( {x - \sqrt x + 1} \right)}}{{\left( {\sqrt x + 1} \right)\left( {\sqrt x - 1} \right)}} - \frac{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}{{\sqrt x + 1}}\\
= \frac{{x - \sqrt x + 1}}{{\sqrt x - 1}} - \left( {\sqrt x - 1} \right)\\
= \frac{{x - \sqrt x + 1 - {{\left( {\sqrt x - 1} \right)}^2}}}{{\sqrt x - 1}}\\
= \frac{{x - \sqrt x + 1 - x + 2\sqrt x - 1}}{{\sqrt x - 1}}\\
= \frac{{\sqrt x }}{{\sqrt x - 1}}.
\end{array}\]
