\( \newcommand{\A}[1]{\colorbox{CornflowerBlue}{$\displaystyle #1$}} \newcommand{\B}[1]{\colorbox{lightgray}{$\displaystyle #1$}} \newcommand{\C}[1]{\colorbox{BurntOrange}{$\displaystyle #1$}} \)

\[\dfrac{1}{x-2}+\dfrac{x-1}{x+2}-1\] \[\dfrac{\A{x+2}}{\A{x+2}} \cdot \dfrac{1}{\B{x-2}}+ \dfrac{\B{x-2}}{\B{x-2}}\cdot \dfrac{x-1}{\A{x+2}}-1\] \[\dfrac{(x+2) \cdot 1}{(x+2)(x-2)} + \dfrac{(x-2)(x-1)}{(x+2)(x-2)}-1\] \[\dfrac{x+2}{(x+2)(x-2)}+\dfrac{x^2-x-2x+2}{(x+2)(x-2)}-1\] \[\dfrac{x+2}{(x+2)(x-2)}+\dfrac{x^2-3x+2}{(x+2)(x-2)}-1\] \[\dfrac{x^2-2x+4}{(x+2)(x-2)}-1\] \[\dfrac{x^2-2x+4}{\C{(x+2)(x-2)}}-\dfrac{\C{(x+2)(x-2)}}{\C{(x+2)(x-2)}}\cdot 1\] \[\dfrac{x^2-2x+4}{(x+2)(x-2)} - \dfrac{(x+2)(x-2)}{(x+2)(x-2)}\] \[\dfrac{x^2-2x+4}{(x+2)(x-2)} - \dfrac{x^2-4}{(x+2)(x-2)}\] \[\dfrac{x^2-2x+4 - (x^2-4)}{(x+2)(x-2)}\] \[\dfrac{x^2-2x+4-x^2+4}{(x+2)(x-2)}\] \[\dfrac{-2x+8}{(x+2)(x-2)}\]

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