问题 解答题
计算
1
2x2+3x-1
-
2
2x2+3x+1
+
1
2x2+3x+3
答案

设2x2+3x=y,则

原式=

1
y-1
-
2
y+1
+
1
y+3

=

(y+1)(y+3)-2(y-1)(y+3)+(y-1)(y+1)
(y-1)(y+1)(y+3)

=

8
(y-1)(y+1)(y+3)

=

8
(2x2+3x-1)(2x2+3x+1)(2x2+3x+3)

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