若关于x的分式方程(1/x-2)+(k/x+2)=4/x^4-4有增根,x=-2,请你求出则k的值

Question

若关于x的分式方程(1/x-2)+(k/x+2)=4/x^4-4 有增根,x=-2,请你求出则k的值

Answer 1

数学之美团为你解答
1/(x-2) + k/(x+2) = 4/(x² -4)
同乘以 x²-4
x+2 +k(x-2) = 4
(k+1)x = 2k+2
有增根 x= -2
代入得 -2(k+1) = 2k+2
解得 k = - 1