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