f(x)=(x²+2x+1)/(x-1)=(x²-2x+1+4x-4+4)/(x-1)=[(x-1)²+4(x-1)+4]/(x-1)=(x-1)+4+4/(x-1)因为x＞1,所以x-1＞0故(x-1)+4/(x-1)≥2√[(x-1)×4/(x-1)]=4,此时x=3故f(x)≥4+4=8所以值域为[8,+∞)...