`A = (sqrt x + 1)/(sqrt x - 2) + ( 2 sqrt x)/(sqrt x +2) + (2 + 5 sqrt x)/(4-x)`
Đk: `x ne 4, x >=0`.
`A = ((sqrt x + 1)(sqrt x +2))/(x - 4) + ((2 sqrt x)(sqrt x-2))/(x-4) - (2+5 sqrt x)/(x-4)`
`= (x + 3 sqrt x + 2 + 2x - 4 sqrt x - 2 - 5 sqrt x)/(x-4)`
`= (3x - 6 sqrt x)/((sqrt x - 2)(sqrt x + 2))`
`= (3 sqrt x(sqrt x - 2))/((sqrtx-2)(sqrtx+2))`
`= (3sqrtx)/(sqrtx+2)`.
đk x ≠4 ; x >0
\(A=\dfrac{\sqrt{x}+1}{\sqrt{x}-2}+\dfrac{2\sqrt{x}}{\sqrt{x}+2}+\dfrac{-2-5\sqrt{x}}{x-4}\\ =\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)+2\sqrt{x}\left(\sqrt{x}-2\right)-2-5\sqrt{x}}{x-4}\\ =\dfrac{x+\sqrt{x}+2\sqrt{x}+2+2x-4\sqrt{x}-2-5\sqrt{x}}{x-4}\\ =\dfrac{3x-6\sqrt{x}}{x-4}\\ =\dfrac{3\sqrt{x}\left(\sqrt{x}-2\right)}{x-4}\\ =\dfrac{3\sqrt{x}}{\sqrt{x}+2}\)
