Giải thích các bước giải:
$\eqalign{ & a)\,P = (\sqrt x - \frac{1}{{\sqrt x }}):(\frac{{\sqrt x - 1}}{{\sqrt x }} - \frac{{\sqrt x - 1}}{{x + \sqrt x }}) \cr & = \frac{{x - 1}}{{\sqrt x }}:(\frac{{\sqrt x - 1}}{{\sqrt x }} - \frac{{\sqrt x - 1}}{{\sqrt x (\sqrt x + 1)}}) \cr & = \frac{{x - 1}}{{\sqrt x }}:\frac{{(\sqrt x - 1)(\sqrt x + 1) - (\sqrt x - 1)}}{{\sqrt x (\sqrt x + 1)}} \cr & = \frac{{x - 1}}{{\sqrt x }}:\frac{{x - 1 - \sqrt x + 1}}{{\sqrt x (\sqrt x + 1)}} \cr & = \frac{{x - 1}}{{\sqrt x }}.\frac{{\sqrt x (\sqrt x + 1)}}{{x - \sqrt x }} \cr & = \frac{{(\sqrt x - 1)(\sqrt x + 1).(\sqrt x + 1)}}{{\sqrt x (\sqrt x - 1)}} \cr & = \frac{{{{(\sqrt x + 1)}^2}}}{{\sqrt x }} \cr} $
b) ĐK: x>0
$\eqalign{ & P = \frac{9}{2} \cr & \Leftrightarrow \frac{{{{(\sqrt x + 1)}^2}}}{{\sqrt x }} = \frac{9}{2} \cr & \Leftrightarrow 2{(\sqrt x + 1)^2} = 9\sqrt x \cr & \Leftrightarrow 2(x + 2\sqrt x + 1) - 9\sqrt x = 0 \cr & \Leftrightarrow 2x - 5\sqrt x + 2 = 0 \cr & \Leftrightarrow (2\sqrt x - 1)(\sqrt x - 2) = 0 \cr & \Leftrightarrow 2\sqrt x - 1 = 0\,hoặc\,\sqrt x - 2 = 0 \cr & \Leftrightarrow \sqrt x = \frac{1}{2}\,hoặc\,\sqrt x = 2 \cr & \Leftrightarrow x = \frac{1}{4}\,hoặc\,x = 4(tm\,x > 0) \cr} $
