问题 解答题
计算:
(1)(x-y+
4xy
x-y
)•(x+y-
4xy
x+y
)

(2)
1
x2+3x+2
+
1
x2+5x+6
+
1
x2+7x+12
答案

(1)(x-y+

4xy
x-y
)•(x+y-
4xy
x+y
)

=

(x+y)2
x-y
(x-y)2
x+y

=(x+y)(x-y)

=x2-y2

(2)

1
x2+3x+2
+
1
x2+5x+6
+
1
x2+7x+12

=

1
(x+1)(x+2)
+
1
(x+2)(x+3)
+
1
(x+3)(x+4)

=

x2+7x+12+x2+5x+4+x2+3x+2
(x+1)(x+2)(x+3)(x+4)

=

3(x+2)(x+3)
(x+1)(x+2)(x+3)(x+4)

=

3
x2+5x+4

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