(1-3x/x^2-1)=(M/x+1)+(N/x-1),求M,N的值

问题描述:

(1-3x/x^2-1)=(M/x+1)+(N/x-1),求M,N的值

右边通分
=[m(x-1)+n(x+1)]/(x+1)(x-1)
=[(m+n)x+(n-m)]/(x+1)(x-1)
=(-3x+1)/(x+1)(x-1)
所以(m+n)x+(n-m)=-3x+1
所以m+n=-3
n-m=1
相加
2n=-2
n=-1
m=n-1=-2