x趋向于无穷时,ax+b-（2x^2-1）／（x-1）的极限为1,求常数a,b.算出了a=2，b算不出来

Question

x趋向于无穷时,ax+b-（2x^2-1）／（x-1）的极限为1,求常数a,b.
算出了a=2，b算不出来

Answer 1

lim【x→∞】ax+b-(2x²-1)/(x-1)
=lim【x→∞】[(ax+b)(x-1)-(2x²-1)]/(x-1)
=lim【x→∞】[(a-2)x²+(b-a)x+1-b]/(x-1)
=lim【x→∞】[(a-2)x+(b-a)+(1-b)/x]/(1-1/x)
因为极限是1
所以a-2=0
b-a=1
解得a=2
b=3