N=(√x - 1/√x ):(√x-1/ √x + 1-√x / x+√x ) Rút gọn

Đáp án:

Giải thích các bước giải: \(\begin{array}{l}\frac{{\sqrt x - 1}}{{\sqrt x }}:\left( {\frac{{\sqrt x - 1}}{{\sqrt x }} + \frac{{1 - \sqrt x }}{{x + \sqrt x }}} \right)\\ = \frac{{\sqrt x - 1}}{{\sqrt x }}:\left( {\frac{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}{{\sqrt x \left( {\sqrt x + 1} \right)}} + \frac{{1 - \sqrt x }}{{\sqrt x \left( {\sqrt x + 1} \right)}}} \right)\\ = \frac{{\sqrt x - 1}}{{\sqrt x }}:\frac{{x - 1 + 1 - \sqrt x }}{{\sqrt x \left( {\sqrt x + 1} \right)}} = \frac{{\sqrt x - 1}}{{\sqrt x }}:\frac{{x - \sqrt x }}{{\sqrt x \left( {\sqrt x + 1} \right)}}\\ = \frac{{\sqrt x - 1}}{{\sqrt x }}:\frac{{\sqrt x \left( {\sqrt x - 1} \right)}}{{\sqrt x \left( {\sqrt x + 1} \right)}} = \frac{{\sqrt x - 1}}{{\sqrt x }}:\frac{{\sqrt x - 1}}{{\sqrt x + 1}}\\ = \frac{{\sqrt x - 1}}{{\sqrt x }}.\frac{{\sqrt x + 1}}{{\sqrt x - 1}} = \frac{{\sqrt x + 1}}{{\sqrt x }}\end{array}\)