问题 解答题
计算:
(1)(x2
b
a
-
xy
a
ab
+
b
a
a
b
)÷x2y2
b
a
(a>0,b>0)

(2)4
x2+xy+y2
x-y
-
1
2
x2-xy+y2
x+y
-3
x3+y3
x3-y3
(x>y>0).
答案

(1)解法一:

原式=x2

1
x2y2
b
a
a
b
-
xy
a
1
x2y2
ab•
a
b
+
b
a
1
x2y2
a
b
a
b

=

1
y2
-
1
xy
+
1
x2y2
=
x2-xy+1
x2y2

解法二:

原式=(

x2
a
ab
-
xy
a
ab
+
1
a
ab
)÷
x2y2
a
ab

=

x2-xy+1
a
ab
a
x2y2
ab

=

x2-xy+1
x2y2

(2)原式=(4×

1
2
×3)
x2+xy+y2
x-y
x2-xy+y2
x+y
(x+y)(x2-xy+y2)
(x-y)(x2+xy+y2)

=6

(x2-xy+y2)2
(x-y)2

=

6x2-6xy+6y2
x-y

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