\(=\dfrac{2x-9}{\left(x-2\right)\left(x-3\right)}-\dfrac{x+3}{x-2}+\dfrac{2x+1}{x-3}\)
\(=\dfrac{2x-9-x^2+9+\left(2x+1\right)\left(x-2\right)}{\left(x-2\right)\left(x-3\right)}\)
\(=\dfrac{-x^2+2x+2x^2-4x+x-2}{\left(x-2\right)\left(x-3\right)}\)
\(=\dfrac{x^2-x-2}{\left(x-2\right)\left(x-3\right)}=\dfrac{x+1}{x-3}\)
\(\dfrac{2x-9}{x^2-5x+6}-\dfrac{x+3}{x-2}-\dfrac{2x+1}{3-x}\left(ĐKXĐ:x\ne2,x\ne3\right)\)
\(=\dfrac{2x-9}{x^2-3x-2x+6}-\dfrac{x+3}{x-2}+\dfrac{2x+1}{x-3}\)
\(=\dfrac{2x-9}{x\left(x-3\right)-2\left(x-3\right)}-\dfrac{x+3}{x-2}+\dfrac{2x+1}{x-3}\)
\(=\dfrac{2x-9}{\left(x-3\right)\left(x-2\right)}-\dfrac{x+3}{x-2}+\dfrac{2x+1}{x-3}\)
\(=\dfrac{2x-9}{\left(x-3\right)\left(x-2\right)}-\dfrac{\left(x+3\right)\left(x-3\right)}{x-2}+\dfrac{\left(2x+1\right)\left(x-2\right)}{x-3}\)
\(=\dfrac{2x-9}{\left(x-3\right)\left(x-2\right)}-\dfrac{x^2-9}{x-2}+\dfrac{2x^2-4x+x-2}{x-3}\)
\(=\dfrac{2x-9-x^2+9+2x^2-4x+x-2}{\left(x-3\right)\left(x-2\right)}\)
\(=\dfrac{x^2-x-2}{\left(x-3\right)\left(x-2\right)}\)
\(=\dfrac{x^2-2x+x-2}{\left(x-3\right)\left(x-2\right)}\)
\(=\dfrac{x\left(x-2\right)+x-2}{\left(x-3\right)\left(x-2\right)}\)
\(=\dfrac{\left(x-2\right)\left(x+1\right)}{\left(x-3\right)\left(x-2\right)}\)
\(=\dfrac{x+1}{x-3}\)
