k是整数,(k^2+2k-3)/(9-k^2)也是整数,求k的值

k是整数,(k^2+2k-3)/(9-k^2)也是整数,求k的值
k是整数,(k^2+2k-3)/(9-k^2)也是整数,求k的值

k是整数,(k^2+2k-3)/(9-k^2)也是整数,求k的值
原式=(k+3)(k-1)/[-(k+3)(k-3)]
=-(k-1)/(k-3)
=-[(k-3+2)/(k-3)]
=-1-2/(k-3)是整数
所以k-3=±1,±3
且分母9-k²≠0
所以k=2,k=4,k=0,k=6