Đáp án:$\frac{(12-\sqrt{x})^{2}}{(\sqrt{x}+1)^{2}(\sqrt{x}-2)}$
Giải thích các bước giải:
3)$([\frac{2\sqrt{x}+3}{(\sqrt{x}+1)(\sqrt{x}-2)}-\frac{4}{\sqrt{x}+1}+\frac{1}{\sqrt{x}-2}]:\frac{\sqrt{x}+1}{12-\sqrt{x}}$
=$[\frac{2\sqrt{x}+3-4(\sqrt{x}-2)+\sqrt{x}+1}{(\sqrt{x}+1)(\sqrt{x}-2)}]·\frac{12-\sqrt{x}}{\sqrt{x}+1}$
=$\frac{2\sqrt{x}+3-4\sqrt{x}+8+\sqrt{x}+1}{(\sqrt{x}+1)(\sqrt{x}-2)}·\frac{12-\sqrt{x}}{\sqrt{x}+1}$
=$\frac{12-\sqrt{x}}{(\sqrt{x}+1)(\sqrt{x}-2)}·\frac{12-\sqrt{x}}{\sqrt{x}+1}$
=$\frac{(12-\sqrt{x})^{2}}{(\sqrt{x}+1)^{2}(\sqrt{x}-2)}$