\(\begin{array}{l} a)A = \dfrac{{{x^2} + \sqrt x }}{{x - \sqrt x + 1}} + \dfrac{{1 - 2x + \sqrt x }}{{\sqrt x }}\\ = \dfrac{{\sqrt x \left( {\sqrt x + 1} \right)\left( {x - \sqrt x + 1} \right)}}{{x - \sqrt x + 1}} + \dfrac{{1 - 2x + \sqrt x }}{{\sqrt x }}\\ = \sqrt x \left( {\sqrt x + 1} \right) + \dfrac{{1 - 2x + \sqrt x }}{{\sqrt x }}\\ = \dfrac{{x\left( {\sqrt x + 1} \right) + 1 - 2x + \sqrt x }}{{\sqrt x }}\\ = \dfrac{{x\sqrt x + x + 1 - 2x + \sqrt x }}{{\sqrt x }}\\ = \dfrac{{x\sqrt x - x + \sqrt x + 1}}{{\sqrt x }}\\ b)A - \left| A \right| = 0\\ \to A = \left| A \right|\\ \to \left[ \begin{array}{l} A = A\left( {ld} \right)\\ A = - A \end{array} \right.\\ \to 2A = 0\\ \to A = 0\\ \to \dfrac{{x\sqrt x - x + \sqrt x + 1}}{{\sqrt x }} = 0\\ \to x\sqrt x - x + \sqrt x + 1 = 0\\ \to \sqrt x = - 0,5436890127\left( l \right) \end{array}\)
