Giải thích các bước giải:
Ta có:
$\dfrac{x^2}{x^2-5x+6}-\dfrac{x}{x^2-4x+3}-\dfrac{3x-2}{x^3-6x^2+11x-6}$
$=\dfrac{x^2}{(x-2)(x-3)}-\dfrac{x}{(x-1)(x-3)}-\dfrac{3x-2}{(x-1)(x-2)(x-3)}$
$=\dfrac{x^2\left(x-1\right)}{\left(x-2\right)\left(x-3\right)\left(x-1\right)}-\dfrac{x\left(x-2\right)}{\left(x-1\right)\left(x-3\right)\left(x-2\right)}-\dfrac{3x-2}{\left(x-2\right)\left(x-3\right)\left(x-1\right)}$
$=\dfrac{x^2\left(x-1\right)-x\left(x-2\right)-\left(3x-2\right)}{\left(x-2\right)\left(x-3\right)\left(x-1\right)}$
$=\dfrac{x^3-2x^2-x+2}{\left(x-2\right)\left(x-3\right)\left(x-1\right)}$
$=\dfrac{\left(x-2\right)\left(x^2-1\right)}{\left(x-2\right)\left(x-3\right)\left(x-1\right)}$
$=\dfrac{x^2-1}{\left(x-3\right)\left(x-1\right)}$
$=\dfrac{\left(x+1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}$
$=\dfrac{x+1}{x-3}$
