Question

已知关于x的方程1/x+2+k/x-1=3/x^2+x-2的解是正整数求整数k的值

Answer 1

1/(x+2)+k/(x-1)=3/(x²+x-2)

1/(x+2)+k/(x-1)=3/(x+2)(x-1)

乘以(x+2)(x-1)得：x-1+k(x+2)=3

x+kx=3+1-2k

(1+k)x=4-2k

x=(4-2k)/(1+k)

x=-2+6/(1+k)

因为解为正整数,∴1+k=1,2,解得x=4或者x=1,此时k=0或者k=1