Toán rút gọn biểu thức (2√x-9)/(x-5√x+6)+(2√x+1)/(√x-3)+(√x+3)/(2-√x) 26/07/2021 By Madelyn rút gọn biểu thức (2√x-9)/(x-5√x+6)+(2√x+1)/(√x-3)+(√x+3)/(2-√x)
$\dfrac{2\sqrt{x}-9}{x-5\sqrt{x}+6}+\dfrac{2\sqrt{x}+1}{\sqrt{x}-3}+\dfrac{\sqrt{x}+3}{2-\sqrt{x}}\\ =\dfrac{2\sqrt{x}-9+(2\sqrt{x}+1)(\sqrt{x}-2)-(\sqrt{x}+3)(\sqrt{x}-3)}{(\sqrt{x}-3)(\sqrt{x}-2)}\\ =\dfrac{2\sqrt{x}-9+2x-3\sqrt{x}-2-x+9}{(\sqrt{x}-3)(\sqrt{x}-2)}\\ =\dfrac{x-\sqrt{x}-2}{(\sqrt{x}-3)(\sqrt{x}-2)}\\ =\dfrac{(\sqrt{x}+1)(\sqrt{x}-2)}{(\sqrt{x}-3)(\sqrt{x}-2)}\\ =\dfrac{\sqrt{x}+1}{\sqrt{x}-3}$ Trả lời
$\dfrac{2\sqrt{x}-9}{x-5\sqrt{x}+6}+\dfrac{2\sqrt{x}+1}{\sqrt{x}-3}+\dfrac{\sqrt{x}+3}{2-\sqrt{x}}\\ =\dfrac{2\sqrt{x}-9+(2\sqrt{x}+1)(\sqrt{x}-2)-(\sqrt{x}+3)(\sqrt{x}-3)}{(\sqrt{x}-3)(\sqrt{x}-2)}\\ =\dfrac{2\sqrt{x}-9+2x-3\sqrt{x}-2-x+9}{(\sqrt{x}-3)(\sqrt{x}-2)}\\ =\dfrac{x-\sqrt{x}-2}{(\sqrt{x}-3)(\sqrt{x}-2)}\\ =\dfrac{(\sqrt{x}+1)(\sqrt{x}-2)}{(\sqrt{x}-3)(\sqrt{x}-2)}\\ =\dfrac{\sqrt{x}+1}{\sqrt{x}-3}$