设a,b∈R~+且a>b,讨论并比较a/b与a+2b/a+b的大小。原题中含有两个变元a、b,为使问题化繁为简,引进新的变元t,且令t=a/b,显然有t>l,则(a+2b)/(a+b)=(t+2)/(t+1)>1,这样,要讨论的两个分式的大小比较就转化为讨论t与(t+2)/(t+1)的大小比较了。 1°设t=t+2/t+1,则有t~2+t=t+2t~2=2,由 Let a, b∈R~+ and a>b, discuss and compare the sizes of a/b and a+2b/a+b. The original question contains two variables a, b, in order to simplify the problem, introduce a new variable t, and let t = a / b, obviously t> l, then (a + 2b) / (a +b)=(t+2)/(t+1)>1. Thus, the comparison of the sizes of the two fractions to be discussed is converted into the size of the discussion t and (t+2)/(t+1). Now. 1° sets t=t+2/t+1, then t~2+t=t+2t~2=2, by