y=(x-1)/(x²+1)＞0;1/y=(x²+1)/(x-1)=(x²-1+2)/(x-1)=x+1+2/(x-1)=2+x-1+2/(x-1);∵x＞1;∴x-1+2/(x-1)≥2√2(x-1)/(x-1)=2√2;∴1/y≥2+2√2;∴y≤1/(2+2√2)=(2√2-2)/4=(√2-1)/2;所以最大值为（...