Explications étape par étape:

on a : BM=BA+AM

c-a-d:BM=BA-1/2AB+3/2AC

BM=-AB-1/2AB+3/2AC

BM=(-1/1-1/2)AB+ 3/2AC

BM= -3/2AB+3/2AC

BM= -3/2 AB+3/2(AB+BC)

BM= -3/2AB+3/2AB+3/2 BC

Donc: BM=3/2 BC