ĐKXĐ: \(x\notin\left\{2;3\right\}\)
\(Q\left(x\right)+\dfrac{x-3}{x-2}-\dfrac{x-2}{x-3}=\dfrac{x-1}{x^2-5x+6}\)
=>\(Q\left(x\right)+\dfrac{\left(x-3\right)^2-\left(x-2\right)^2}{\left(x-2\right)\left(x-3\right)}=\dfrac{x-1}{\left(x-2\right)\left(x-3\right)}\)
=>\(Q\left(x\right)+\dfrac{x^2-6x+9-x^2+4x-4}{\left(x-2\right)\left(x-3\right)}=\dfrac{x-1}{\left(x-2\right)\left(x-3\right)}\)
=>\(Q\left(x\right)+\dfrac{-2x+5}{\left(x-2\right)\left(x-3\right)}=\dfrac{x-1}{\left(x-2\right)\left(x-3\right)}\)
=>\(Q\left(x\right)=\dfrac{x-1-\left(-2x+5\right)}{\left(x-2\right)\left(x-3\right)}=\dfrac{3x-6}{\left(x-2\right)\left(x-3\right)}\)
=>\(Q\left(x\right)=\dfrac{3}{x-3}\)
đk x khác 2;3
\(Q\left(x\right)=\dfrac{x-1}{\left(x-2\right)\left(x-3\right)}+\dfrac{x^2-6x+9}{\left(x-2\right)\left(x-3\right)}-\dfrac{x^2-4x+4}{\left(x-2\right)\left(x-3\right)}\)
\(=\dfrac{x-1-2x+5}{\left(x-2\right)\left(x-3\right)}=\dfrac{-x+4}{\left(x-2\right)\left(x-3\right)}\)
