Given that f(x)=x2008−2x2007+3x2006−4x2005+⋯+2007x2−2008x+2009f(x)=x^{2008}-2x^{2007}+3x^{2006}-4x^{2005}+\cdots+2007x^2-2008x+2009f(x)=x2008−2x2007+3x2006−4x2005+⋯+2007x2−2008x+2009 and that g(x)=2012x+2009(1+x)2,g(x)=\frac{2012x+2009}{(1+x)^2},g(x)=(1+x)22012x+2009, which of the following is a solution to g(x)=f(x)g(x)=f(x)g(x)=f(x)? A111B21/20092^{1/2009}21/2009C31/20093^{1/2009}31/2009D41/20094^{1/2009}41/2009E21/20082^{1/2008}21/2008F31/20083^{1/2008}31/2008G41/20084^{1/2008}41/2008