$A=\dfrac{x+1-2\sqrt{x}}{\sqrt{x}-1}+\dfrac{x+\sqrt{x}}{\sqrt{x}+1}\\ =\dfrac{(\sqrt{x}-1)^2}{\sqrt{x}-1}+\dfrac{\sqrt{x}(\sqrt{x}+1)}{\sqrt{x}+1}\\ =\sqrt{x}-1+\sqrt{x}\\ =2\sqrt{x}-1\\ B=\dfrac{1}{2\sqrt{x}-2}-\dfrac{1}{2\sqrt{x}+2}+\dfrac{\sqrt{x}}{1-x}\\ =\dfrac{\sqrt{x}+1}{2(\sqrt{x}-1)(\sqrt{x}+1)}-\dfrac{\sqrt{x}-1}{2(\sqrt{x}-1)(\sqrt{x}+1)}-\dfrac{2\sqrt{x}}{2(x-1)}\\ =\dfrac{\sqrt{x}+1-\sqrt{x}+1-2\sqrt{x}}{2(x-1)}\\ =\dfrac{2-2\sqrt{x}}{2(x-1)}\\ =\dfrac{-1}{\sqrt{x}+1}\\ C=\dfrac{\sqrt{x}+1}{\sqrt{x}-2}+\dfrac{2\sqrt{x}}{\sqrt{x}+2}+\dfrac{2+5\sqrt{x}}{4-x}\\ =\dfrac{(\sqrt{x}+1)(\sqrt{x}+2)}{(\sqrt{x}-2)(\sqrt{x}+2)}+\dfrac{2\sqrt{x}(\sqrt{x}-2)}{(\sqrt{x}-2)(\sqrt{x}+2)}-\dfrac{2+5\sqrt{x}}{x-4}\\ =\dfrac{x+3\sqrt{x}+2+2x-4\sqrt{x}-2-5\sqrt{x}}{x-4}\\ =\dfrac{3x-6\sqrt{x}}{x-4}\\ =\dfrac{3\sqrt{x}(\sqrt{x}-2)}{(\sqrt{x}-2)(\sqrt{x}+2)}\\ =\dfrac{3\sqrt{x}}{\sqrt{x}+2}$
