已知x+5/(x+1)(x-3)=a/x+1+b/x-3,求整式A,B的值

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已知x+5/(x+1)(x-3)=a/x+1+b/x-3,求整式A,B的值已知x+5/(x+1)(x-3)=a/x+1+b/x-3,求整式A,B的值已知x+5/(x+1)(x-3)=a/x+1+b/x

已知x+5/(x+1)(x-3)=a/x+1+b/x-3,求整式A,B的值
已知x+5/(x+1)(x-3)=a/x+1+b/x-3,求整式A,B的值

已知x+5/(x+1)(x-3)=a/x+1+b/x-3,求整式A,B的值
右边通分
=[a(x-3)+b(x+1)]/(x+1)(x-3)
=[(a+b)x+(b-3a)]/(x+1)(x-3)
=(x+5)/(x+1)(x-3)
所以(a+b)x+(b-3a)=x+5
所以
a+b=1
b-3a=5
所以a=-1,b=2

dd

以分母为(x+1)(x-3)通分,得到两边分子相等:
x+5=a(x-3)+b(x+1)=(a+b)x+b-3a
对比各项,得
a+b=1
b-3a=5
所以
b=2,a=-1

(x+5)/(x+1)(x-3)=a/(x+1)+b/(x-3)
=> (x+5) = a(x-3)+b(x+1)
put x=3
8=4b
b=2
put x=-1
4=-4a
a=-1