[tex]\frac{2x^{2} + 3x -2}{2x^{3} + x^{2} + 6x+3} : \frac{4x^{2} -1}{4x^{2} +4x +1} \\\frac{2x^{2} + 3x -2}{x^{2} ( 2x+1) + 3( 2x+1)}* \frac{(2x+1)^{2} }{( 2x-1) (2x+1)} \\\frac{2x^{2} + 3x -2}{(2x+1) ( x^{2} +3)} * \frac{(2x+1)^{2} }{( 2x-1) (2x+1)} \\\\\\\frac{2x^{2} + 3x -2}{ ( x^{2} +3)} * \frac{1 }{( 2x-1)}\\\\\frac{4x^{3}- 2x^{2} +6x^{2} -3x +4x+2}{x^{2} + 3} \\\frac{4x^{3} + 4x^{2} +x +2}{x^{2} + 3}[/tex]
