`A = (2x-9)/(x^2-5x+6) - (x+3)/(x-2) - (2x+4)/(3-x)`
ĐKXĐ : `x^2 - 5x + 6 \ne 0 , x - 2 \ne 0 , 3 - x \ne 0`
Ta có : `x^2 - 5x + 6 = (x^2-2x)+(-3x+6) = x(x-2)-3(x-2) = (x-2)(3-x)`
`⇒`ĐKXĐ là : `x - 2 \ne 0 , 3 - x \ne 0`
`⇒ x \ne 2 , x \ne 3`
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`A = (2x-9)/(x^2-5x+6) - (x+3)/(x-2) - (2x+4)/(3-x)`
`= (2x-9)/(x^2-2x-3x+6) - (x+3)/(x-2) - (2x+4)/(-(x-3))`
`= (2x-9)/(x(x-2)-3(x-2)) - (x+3)/(x-2) + (2x+4)/(x-3)`
`= (2x-9-(x-3)(x+3)+(x-2)(2x+4))/((x-2)(x+3))`
`= (2x-9-(x^2-9)+2x^2+4x-4x-8)/((x-2)(x+3))`
`= (2x-9-x^2+9+2x^2-8)/((x-2)(x+3))`
`= (2x+x^2-8)/((x-2)(x-3))`
`= (x^2+4x-2x-8)/((x-2)(x-3))`
`= (x(x+4)-2(x+4))/((x-2)(x-3))`
`= ((x+4)(x-2))/((x-2)(x-3)`
`= (x+4)/(x-3)`
