已知A、B是常数,若分式X+2分之A与X-2分之B的和是X平方减4分之4X,则A＝?,B＝?.

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[A/(x+2)]+[B/(x-2)]=4x/(x²-4)
通分得[A(x-2)+B(x+2)]/(x²-4)=4x/(x²-4)
[(A+B)x+2B-2A]/(x²-4)=4x/(x²-4)
(A+B)x+2B-2A=4x
比较系数得A+B=42B-2A=0
解得A=B=2
======以下答案可供参考======
供参考答案1:
A=2,B=2
供参考答案2:
A/(X+2)+B/(X-2)=4X/(X^2-4)
A(X-2)+B(X+2)=4X
A+B=42B-2A=0
A=B=2供参考答案3:
A/(x+2)+B/(x-2)=4x/(x^2-4)
[A(x-2)+B(x+2)]/(x^2-4)=4x/(x^2-4)
[(A+B)x+2B-2A]/(X62-4)=4x/(x^2-4)
则 A+B=4 2B-2A=0
则 A=2=B供参考答案4:
https://zhidao.baidu./question/49704095.html