Question

Chứng minh:

\(\left(\frac{2-x\sqrt{x}}{2-\sqrt{x}}+\sqrt{x}\right).\frac{2-\sqrt{x}}{2-x}=\sqrt{x}+1\)

Answer 1

\( VT = \left( {\dfrac{{2 - x\sqrt x }}{{2 - \sqrt x }} + \sqrt x } \right).\dfrac{{2 - \sqrt x }}{{2 - x}}\\ = \dfrac{{2 - x\sqrt x + \sqrt x \left( {2 - \sqrt x } \right)}}{{2 - \sqrt x }}.\dfrac{{2 - \sqrt x }}{{2 - x}}\\ = \left( {2 - x\sqrt x + 2\sqrt x - x} \right).\dfrac{1}{{2 - x}}\\ = \dfrac{{2\left( {1 + \sqrt x } \right) - x\left( {\sqrt x + 1} \right)}}{{2 - x}}\\ = \dfrac{{\left( {\sqrt x + 1} \right)\left( {2 - x} \right)}}{{2 - x}} = \sqrt x + 1 = VP \text{(đpcm)} \)