kill(all)$

van=facebook.com/LearningCalculus$

f(x):=((x+1)/(x-1))^x;
g(a,b,x):=((x)/(x-1))^(a*x+b);

van=facebook.com/LearningCalculus$

limit(g(a,b,x),x,inf);

limit(f(x)/g(a,b,x),x,inf);

subst(2,a,%);

float(%e^2);