Rút gọn biểu thức căn x - 2/ x - 1

Rút gọn biểu thức:

$(\frac{\sqrt{x}-2 }{x-1} -\frac{\sqrt{x}+2 }{x+2\sqrt{x}+1}).(\dfrac{1-x}{\sqrt{2} } )$

1 Câu trả lời

Đường tăng
$\begin{matrix} \left( {\frac{{\sqrt x - 2}}{{x - 1}} - \frac{{\sqrt x + 2}}{{x + 2\sqrt x + 1}}} \right).{\left( {\frac{{1 - x}}{{\sqrt 2 }}} \right)^2} \hfill \\ = \left[ {\frac{{\sqrt x - 2}}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}} - \frac{{\sqrt x + 2}}{{{{\left( {\sqrt x + 1} \right)}^2}}}} \right].{\left( {\frac{{1 - x}}{{\sqrt 2 }}} \right)^2} \hfill \\ = \left[ {\frac{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 1} \right)}}{{\left( {\sqrt x - 1} \right){{\left( {\sqrt x + 1} \right)}^2}}} - \frac{{\left( {\sqrt x + 2} \right)\left( {\sqrt x - 1} \right)}}{{\left( {\sqrt x - 1} \right){{\left( {\sqrt x + 1} \right)}^2}}}} \right].{\left( {\frac{{1 - x}}{{\sqrt 2 }}} \right)^2} \hfill \\ \end{matrix}$
$\begin{matrix} = \left[ {\frac{{x - \sqrt x - 2 - x - \sqrt x + 2}}{{\left( {\sqrt x - 1} \right){{\left( {\sqrt x + 1} \right)}^2}}}} \right].{\left( {\frac{{x - 1}}{{\sqrt 2 }}} \right)^2} \hfill \\ = \left[ {\frac{{ - 2\sqrt x }}{{\left( {\sqrt x - 1} \right){{\left( {\sqrt x + 1} \right)}^2}}}} \right].{\left( {\frac{{x - 1}}{{\sqrt 2 }}} \right)^2} \hfill \\ = \left[ {\frac{{ - 2\sqrt x }}{{\left( {\sqrt x - 1} \right){{\left( {\sqrt x + 1} \right)}^2}}}} \right].{\left( {\frac{{x - 1}}{{\sqrt 2 }}} \right)^2} \hfill \\ = \frac{{ - \sqrt x }}{{\sqrt x - 1}} \hfill \\ \end{matrix}$
0 Trả lời 12/08/22