若不等式x+2/k＞1+ (x-3)/k的解是x＞3,求k的值

若不等式x+2/k＞1+ (x-3)/k的解是x＞3,求k的值
若不等式x+2/k＞1+ (x-3)/k的解是x＞3,求k的值

若不等式x+2/k＞1+ (x-3)/k的解是x＞3,求k的值
(x+2)/k>1+(x-3)/k²
k(x+2)>k²+x-3
(k-1)x>k²-2k-3
解是x>3,说明k-1>0,且3(k-1)=k²-2k-3
k²-5k=0,k(k-5)=0,k=5,或k=0
而k-1>0,即k>1,所以k=5

x+2/k＞1+ (x-3)/k
(k-1)x-3k+1-2/k<0
(k-1)x<3k-1+2/k
因为x>3
所以k-1<0,k<1
x>(3k-1+2/k)/(k-1)
(3k-1+2/k)/(k-1)=3
3k-1+2/k=3k-3
2/k=-2
k=-1