问题 解答题
观察下列式子:
1
2
+1
=
2
-1
(
2
+1)(
2
-1)
=
2
-1

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

1
4
+
3
=
4
-
3
(
4
+
3
)(
4
-
3
)
=
4
-
3

试求:(1)
1
11
+
10
的值;
(2)
1
3
2
+
17
的值;
(3)针对上述各式反映的规律,写出用n(n为正整数)表示的等式.
答案

(1)

1
11
+
10

=

11
-
10
(
11
+
10)(
11
-
10
)

=

11
-
10

(2)

1
3
2
+
17

=

3
2
-
17
(3
2
+
17
)(3
2
-
17
)

=3

2
-
17

(3)

1
n+1
+
n

=

n+1
-
n

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