(x^2 /(x^2 -5*x+6))-(x/(x^2 -4*x+3))-((3*x-2)/(x^3 -6*x^2 +11*x-6))

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1. Giải thích các bước giải:

   Ta có:

   $\dfrac{x^2}{x^2-5x+6}-\dfrac{x}{x^2-4x+3}-\dfrac{3x-2}{x^3-6x^2+11x-6}$

   $=\dfrac{x^2}{(x-2)(x-3)}-\dfrac{x}{(x-1)(x-3)}-\dfrac{3x-2}{(x-1)(x-2)(x-3)}$

   $=\dfrac{x^2\left(x-1\right)}{\left(x-2\right)\left(x-3\right)\left(x-1\right)}-\dfrac{x\left(x-2\right)}{\left(x-1\right)\left(x-3\right)\left(x-2\right)}-\dfrac{3x-2}{\left(x-2\right)\left(x-3\right)\left(x-1\right)}$

   $=\dfrac{x^2\left(x-1\right)-x\left(x-2\right)-\left(3x-2\right)}{\left(x-2\right)\left(x-3\right)\left(x-1\right)}$
   $=\dfrac{x^3-2x^2-x+2}{\left(x-2\right)\left(x-3\right)\left(x-1\right)}$

   $=\dfrac{\left(x-2\right)\left(x^2-1\right)}{\left(x-2\right)\left(x-3\right)\left(x-1\right)}$

   $=\dfrac{x^2-1}{\left(x-3\right)\left(x-1\right)}$

   $=\dfrac{\left(x+1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}$

   $=\dfrac{x+1}{x-3}$

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