[tex]\displaystyle\bf\\2x^{2} +x-3=0\\\\D=1^{2} -4\cdot 2\cdot(-3)=1+24=25=5^{2} \\\\\\x_{1} =\frac{-1-5}{4} =\frac{-6}{4}=-1,5\\\\\\x_{2} =\frac{-1+5}{4} =\frac{4}{4} =1\\\\\\\boxed{2x^{2} +x-3=2\cdot(x+1,5)\cdot(x-1)}\\\\\\\frac{2x^{2} +x-3}{x^{2} -2x+1} =\frac{2\cdot(x+1,5)\cdot(x-1)}{(x-1)^{2} } =\frac{2\cdot(x+1,5)}{x-1} =\frac{2x+3}{x-1}[/tex]