$\begin{array}{l} \dfrac{{x + \sqrt x }}{{\sqrt x }} + \dfrac{{x - 1}}{{\sqrt x + 1}} - \dfrac{{x - 4}}{{\sqrt x - 2}}\\ = \dfrac{{\sqrt x \left( {\sqrt x + 1} \right)}}{{\sqrt x }} + \dfrac{{\left( {\sqrt x + 1} \right)\left( {\sqrt x - 1} \right)}}{{\sqrt x + 1}} - \dfrac{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}{{\sqrt x - 2}}\\ = \sqrt x + 1 + \sqrt x - 1 - \left( {\sqrt x + 2} \right)\\ = 2\sqrt x - \sqrt x - 2\\ = \sqrt x - 2 \end{array}$
