这些题目都用作差法.
1.
(a+b)/b-(c+d)/d (通分)
=[(a+b)d-(c+d)b]/(bd)
=(ad-bc)/(bc) (ad-bc≥0,bc>0)
≥0
即 (a+b)/b≥(c+d)/d.
2.
a/(c-a)-b/(c-b) (通分)
=[a(c-b)-b(c-a)]/[(c-a)(c-b)]
=(ac-bc)/[(c-a)(c-b)]
=c(a-b)/[(c-a)(c-b)] (c>0,a-b>0,c-a>0,c-b>0)
>0
即 a/(c-a)>b/(c-b).
3.
(a+m)/(b+m)-a/b (通分)
=[(a+m)b-a(b+m)]/[b(b+m)]
=m(b-a)/[b(b+m)] (m>0,b-a>0,b>0,b+m>0)
>0
即 (a+m)/(b+m)>a/b.