右边=[M(x-5)+N(x+1)]/(x+1)(x-5)
=[(M+N)x+(N-5M)]/(x²-4x-5)
=(7x+8)/(x²-4x-5)
所以(M+N)x+(N-5M)=7x+8
所以M+N=7
N-5M=8
M=-1/6,N=43/6