Bonjour

a/b < c/d
ad < bc

(a+c)/(b+d) - a/b = (ab+bc)/[b(b+d)] - (ab+ad)/[b(b+d)] = (ab+bc-ab-ad)/[b(b+d)] = (bc-ad)/[b(b+d)] > 0
et
(a+c)/(b+d) - c/d = (ad+cd)/[d(b+d)] - (bc+cd)/[d(b+d)] = (ad+cd-bc-cd)/[d(b+d)] = (ad-bc)/[d(b+d)] < 0