$a) \left ( \dfrac{2x+1}{\sqrt{x^{3}}-1}-\dfrac{\sqrt{x}}{x+\sqrt{x}+1} \right )\left ( \dfrac{1+\sqrt{x^{3}}}{1+\sqrt{z}}-\sqrt{x} \right )\\=\left ( \dfrac{2x+1}{x\sqrt{x}-1}-\dfrac{\sqrt{x}}{x+\sqrt{x}+1} \right )\left ( \dfrac{1+x\sqrt{x}}{1+\sqrt{x}}-\sqrt{x} \right )\\=\left ( \dfrac{2x+1}{(\sqrt{x}-1)(x+\sqrt{x}+1)}-\dfrac{\sqrt{x}}{x+\sqrt{x}+1} \right )\left ( \dfrac{(1+\sqrt{x})(1-1\sqrt{x}+x)}{1+\sqrt{x}}-\sqrt{x} \right )\\=\dfrac{2x+1-(\sqrt{x}-1)\sqrt{x}}{(\sqrt{x}-1)(x+\sqrt{x}+1)}(1-\sqrt{x}+x-\sqrt{x})\\=\dfrac{2x+1-(x-\sqrt{x})}{(\sqrt{x}-1)(x+\sqrt{x}+1)}(1-2\sqrt{x}+x)\\=\dfrac{2x+1-x+\sqrt{x}}{(\sqrt{x}-1)(x+\sqrt{x}+1)}(1-\sqrt{x})^{2}\\=\dfrac{x+1+\sqrt{x}}{(\sqrt{x}-1)(x+\sqrt{x}+1)}[-(\sqrt{x}-1)]^{2}\\=\dfrac{1}{\sqrt{x}-1}(\sqrt{x}-1)^{2}\\=\sqrt{x}-1\\b)\left ( 1+\dfrac{\sqrt{x}}{x+1} \right ):\left ( \dfrac{2\sqrt{x}}{x+1-x\sqrt{x}-\sqrt{x}}-\dfrac{1}{1-\sqrt{x}} \right )\\=\dfrac{x+1+\sqrt{x}}{x+1}\left ( \dfrac{2\sqrt{x}}{-(-x-1)+\sqrt{x}(-x-1)}-\dfrac{1}{1-\sqrt{x}} \right )\\=\dfrac{x+1+\sqrt{x}}{x+1}:\left ( \dfrac{2\sqrt{x}}{-(-x-1)(1-\sqrt{x})}-\dfrac{1}{1-\sqrt{x}} \right )\\=\dfrac{x+1+\sqrt{x}}{x+1}:\left ( \dfrac{2\sqrt{x}}{(-x-1)(1-\sqrt{x})}-\dfrac{1}{1-\sqrt{x}} \right )\\=\dfrac{x+1+\sqrt{x}}{x+1}:\left ( -\dfrac{2\sqrt{x}-x-1}{(-x-1)(1-\sqrt{x})} \right )\\=\dfrac{x+1+\sqrt{x}}{x+1}\left ( -\dfrac{(-x-1)(1-\sqrt{x})}{2\sqrt{x}-x-1} \right )\\=-\dfrac{x+1+\sqrt{x}}{x+1}.\dfrac{-(x+1)(1-\sqrt{x})}{2\sqrt{x}-x-1}\\=-(x+1+\sqrt{x})\dfrac{-(1-\sqrt{x})}{2\sqrt{x}-x-1}\\=\dfrac{(x+1+\sqrt{x})(1-\sqrt{x})}{2\sqrt{x}-x-1}\\=\dfrac{x-x\sqrt{x}+1-\sqrt{x}+\sqrt{x}-x}{2\sqrt{x}-x-1}\\=\dfrac{-x\sqrt{x}+1}{2\sqrt{x}-x-1}$
