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

\[\dfrac{1}{4x+1}-\dfrac{1}{3}+\dfrac{1}{2x-3}\] \[\dfrac{\B{3}}{\B{3}} \dfrac{\C{2x-3}}{\C{2x-3}} \cdot \dfrac{1}{\A{4x+1}} -\dfrac{\A{4x+1}}{\A{4x+1}} \dfrac{\C{2x-3}}{\C{2x-3}} \cdot \dfrac{1}{\B{3}} +\dfrac{\A{4x+1}}{\A{4x+1}} \dfrac{\B{3}}{\B{3}} \cdot \dfrac{1}{\C{2x-3}}\] \[\dfrac{3(2x-3)}{3(4x+1)(2x-3)} -\dfrac{(4x+1)(2x-3)}{3(4x+1)(2x-3)} + \dfrac{3(4x+1)}{3(4x+1)(2x-3)}\] \[\dfrac{6x-9}{3(4x+1)(2x-3)} -\dfrac{8x^2-12x+2x-3}{3(4x+1)(2x-3)} +\dfrac{12x+3}{3(4x+1)(2x-3)}\] \[\dfrac{6x-9}{3(4x+1)(2x-3)} -\dfrac{8x^2-10x-3}{3(4x+1)(2x-3)} +\dfrac{12x+3}{3(4x+1)(2x-3)}\] \[\dfrac{6x-9-(8x^2-10x-3)+12x+3}{3(4x+1)(2x-3)}\] \[\dfrac{6x-9-8x^2+10x+3+12x+3}{3(4x+1)(2x-3)}\] \[\dfrac{-8x^2 + 28x -3}{3(4x+1)(2x-3)}\]

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