∵0＜x＜1,a,b為正實數(shù) ∴1-x＜0 ∴b/(x-1)+(x-1)≥ 2√b ∴b/(1-x)+(1-x)≤2 √b ∵a/x+x≥2 √a ∴a/x+x+b/(1-x)+(1-x)=a/x+b/(1-x)+1≥2√a+2√b ∴當(dāng)0＜x＜1時,a/x+b/(1-x)≥2√a+2√b-1 ∴a/x+b/1-x的最小值為2√a+2√b-1