$\displaystyle \begin{array}{{>{\displaystyle}l}} A=\left(\frac{2\sqrt{x} +x}{x\sqrt{x} -1} -\frac{1}{\sqrt{x} -1}\right) :\frac{\sqrt{x} +2}{x+\sqrt{x} +1}\\ DK\ :\ x\geqslant 0;\ x\#1\ \\ A=\frac{2\sqrt{x} +x-x-\sqrt{x} -1}{\left(\sqrt{x} -1\right)\left( x+\sqrt{x} +1\right)} .\frac{x+\sqrt{x} +1}{\sqrt{x} +2}\\ A=\frac{\sqrt{x} -1}{\sqrt{x} -1} .\frac{1}{\sqrt{x} +2} =\frac{1}{\sqrt{x} +2} \ \\ b) \ A=\left(\frac{x}{\sqrt{x} -1} -\sqrt{x}\right) :\left(\frac{\sqrt{x} +1}{\sqrt{x}} -\frac{1}{1-\sqrt{x}} +\frac{2-x}{x-\sqrt{x}}\right)\\ DK\ :x\#1;\ x\geqslant 0\\ A=\frac{x-x+\sqrt{x}}{\sqrt{x} -1} :\left(\frac{\left(\sqrt{x} +1\right)\left(\sqrt{x} -1\right) +\sqrt{x} +2-x}{\sqrt{x}\left(\sqrt{x} -1\right)}\right)\\ A=\frac{\sqrt{x}}{\sqrt{x} -1} .\frac{\sqrt{x}\left(\sqrt{x} -1\right)}{x-1+\sqrt{x} +2-x}\\ A=\frac{x}{\sqrt{x} +1} \end{array}$
