对于各级数学竞赛中一类分式型不等式,如果将其分母换元,然后用新元素表示各个量,将复杂问题转化为已知的或简单的问题进行解决,能够达到事半功倍的目的,现举例说明,以飨读者.例1已知a、b、c∈R+,求证:a b+c+b c+a+c a+b≥32.(第26届莫斯科数学奥林匹克试题) For a class of fractional inequalities in mathematics contests at all levels, if the denominator is replaced by a new one and then the new elements are used to represent each quantity, the complicated problem can be transformed into a known or simple problem to be solved, For example, to read the reader. Example 1 known a, b, c ∈ R +, verify: a b + c + b c + a + c a + b ≥ 32. (26th Moscow Mathematical Olympiad)