f(x)=(2x)/(x-1)={2(x-1)+2}/(x-1) =2+2/(x-1) 因为x在区间(1,无穷)上,所以 x-1>0即f(x)在区间(1,无穷)单调递减
f(x)=2+2/(x-1)假设x1,x2在定义的区间内,且x1f(x2)-f(x1)=2/(x2-1)-2/(x1-1)={2(x1-1)-2(x2-1)}/{(x2-1)(x1-1)}=2(x1-x2)/{(x2-1)(x1-1)}<0所以单调递减