问题 填空题
x+6
x2-4
=
A
x+2
+
B
x-2
成立,则A=______;B=______.
答案

x+6
x2-4
=
A
x+2
+
B
x-2

x+6
(x+2)(x-2)
=
A(x-2)
(x+2)(x-2)
+
B(x+2)
(x+2)(x-2)

x+6
(x+2)(x-2)
=
A(x-2)+B(x+2)
(x+2)(x-2)

x+6
(x+2)(x-2)
=
(A+B)x+(-2A+2B)
(x+2)(x-2)

A+B=1
-2A+2B=6

解得:A=-1,B=2,

故答案为:-1,2.

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