若x^1/2+x^-1/2=3,求（x^3/2+x^-3/2 -3)/(x^2+x^-2 -2)的值
问题描述：
若x^1/2+x^-1/2=3,求（x^3/2+x^-3/2 -3)/(x^2+x^-2 -2)的值
答
x^1/2+x^-1/2=3 两边平方得：x+2+x^-1=9,x+x^-1=7, 两边再平方得：x^2+2+x^-2=49,x^2+x^-2=47 （x^3/2+x^-3/2 -3)/(x^2+x^-2 -2) =[（x^1/2+x^-1/2）（x-1+x^-1）-3 ]/(x^2+x^-2 -2) =[3 ×6-3]/（47-2） =15/45 =1/3