|x|>1,|y|>1,x,y∈R,求证|（x-y）/（1-xy）|

①
x-y x-y+1-xy (1+x)(1-y)
—— + 1 = ———— = —————
1-xy 1-xy 1-xy
∵|x|>1 |y|>1
∴x1
y1
若x0,xy0
(1+x)(1-y)
————— > 0
1-xy
若x>1,y>1,则1+x>0,1-y1,1-xy 0
1-xy
即：
x-y (1+x)(1-y)
—— + 1 = ————— > 0
1-xy 1-xy
x-y
—— > -1
1-xy
②
x-y x-y-1+xy (x-1)(y+1)
—— - 1 = ———— = —————
1-xy 1-xy 1-xy
∵|x|>1 |y|>1
∴x1
y1
若x0,xy>1,1-xy