问题 填空题
已知:
3x-4
x2-3x+2
=
A
x-1
+
B
x-2
,则A=______;B=______.
答案

A
x-1
+
B
x-2
=
A(x-2)+B(x-1)
(x-1)(x-2)
=
(A+B)x-(2A+B)
(x-1)(x-2)

3x-4
x2-3x+2
=
3x-4
(x-1)(x-2)
=
A
x-1
+
B
x-2

∴3x-4=(A+B)x-(2A+B),

A+B=3
2A+B=4

解得:

A=1
B=2

故答案为:1,2.

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