(2x+1)/(x-1)
=[2(x-1)+3]/(x-1)
=2+[3/(x-1)]
x∈[0,1)∪(1,2]
x-1∈[-1,0)∪(0,1]
3/(x-1)∈(-∞,-3]∪[3,+∞)
y∈(-∞,1]∪[5,+∞)