若A/(x+2)与B/(x-2)的和等于2x\x²-4
问题描述:
若A/(x+2)与B/(x-2)的和等于2x\x²-4
答
A/(A+2)+B/(X-2)
=[A(X-2)+B(X+2)]/(X^2-4)
=[(A+B)X+(-2A+2B)]/(X^2-4)
比较系数得方程组:
A+B=2
-2A+2B=0
解得:A=B=1.