问题 解答题
计算下列各题:
(1)
1
x-3
+
6
9-x2
-
x-1
6-2x

(2)(
x+2y
x+y
-
x
y
)÷(
x
y
+2-
x
x-y
)
答案

(1)

1
x-3
+
6
9-x2
-
x-1
6-2x

=

2(x+3)
2(x2-9)
-
12
2(x2-9)
+
(x-1)(x+3)
2(x2-9)

=

2x+6-12+x2+3x-x-3
2(x2-9)

=

x2+4x-9
2(x2-9)

(2)(

x+2y
x+y
-
x
y
)÷(
x
y
+2-
x
x-y
),

=

y(x+2y)-x(x+y)
y(x+y)
÷
x(x-y)+2y(x-y)-xy
y(x-y)

=

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

=-

x-y
x+y

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