\(A = \left( {\dfrac{3}{{2x + 4}} + \dfrac{x}{{2 - x}} - \dfrac{{2{x^2} + 3}}{{{x^2} - 4}}} \right):\dfrac{{2x - 1}}{{4x - 8}}\\ A = \left[ {\dfrac{3}{{2\left( {x + 2} \right)}} - \dfrac{x}{{x - 2}} - \dfrac{{2{x^2} + 3}}{{\left( {x - 2} \right)\left( {x + 2} \right)}}} \right].\dfrac{{4x - 8}}{{2x - 1}}\\ A = \dfrac{{3\left( {x - 2} \right) - 2x\left( {x + 2} \right) - 2\left( {2{x^2} + 3} \right)}}{{2\left( {x - 2} \right)\left( {x + 2} \right)}}.\dfrac{{4\left( {x - 2} \right)}}{{2x - 1}}\\ A = \dfrac{{3x - 6 - 2{x^2} - 4x - 4{x^2} - 6}}{{x + 2}}.\dfrac{2}{{2x - 1}}\\ A = \dfrac{{ - x - 12 - 6{x^2}}}{{x + 2}}.\dfrac{2}{{2x - 1}}\\ A = \dfrac{{ - 2x - 24 - 12{x^2}}}{{2{x^2} - x + 4x - 2}}\\ A = \dfrac{{ - 12{x^2} - 2x - 24}}{{2{x^2} + 3x - 2}}\\ \)
