问题 解答题
阅读下面问题:

1
1+
2
=
1×(
2
-1)
(
2
+1)(
2
-1)
=
2
-1

1
3
+
2
=
3
-
2
(
3
+
2
)(
3
-
2
)
=
3
-
2

1
5
+2
=
5
-2
(
5
+2)(
5
-2)
=
5
-2

试求:
(1)
1
7
+
6
的值;(2)
1
n+1
+
n
(n为正整数)的值.
答案

(1)

1
7
+
6
=
7
-
6
(
7
+
6
)(
7
-
6
)
=
7
-
6

(2)

1
n+1
+
n
=
n+1
-
n
(
n+1
+
n
)(
n+1
-
n
)
=
n+1
-
n

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