a为整数,2a-1≠0
(6a-3)/(4a²-1)
=3(2a-1)/[(2a+1)(2a-1)]
=3/(2a+1)
要分式的值为整数,3能被2a+1整除.
3的因子只有-3、-1、1、3
令2a+1=-3,解得a=-2
令2a+1=-1,解得a=-1
令2a+1=1,解得a=0
令2a+1=3,解得a=1
综上,得a共4个-2,-1,0,1
a为整数,2a-1≠0
(6a-3)/(4a²-1)
=3(2a-1)/[(2a+1)(2a-1)]
=3/(2a+1)
要分式的值为整数,3能被2a+1整除.
3的因子只有-3、-1、1、3
令2a+1=-3,解得a=-2
令2a+1=-1,解得a=-1
令2a+1=1,解得a=0
令2a+1=3,解得a=1
综上,得a共4个-2,-1,0,1