问题 解答题
请看有理化分母:
(一)
3
5
=
5
5
×
5
=
3
5
5

(二)
2
3
=
2×3
3×3
=
6
3

(三)
2
3
+1
=
2(
3
-1)
(
3
+1)(
3
-1)
=
2(
3
-1)
(
3
)2-12
=
3
-1

(四)
2
3
+1
=
3-1
3
+1
=
(
3
)
2
-12
3
+1
=
(
3
+1)(
3
-1)
3
+1
=
3
-1

(1)请用不同的方法化简
2
5
+
3

(2)化简
1
3
+1
+
1
5
+
3
+
1
7
+
5
+…+
1
2n+1
+
2n-1
答案

(1)方法一:

2
5
+
3
=
2(
5
-
3
)
(
5
+
3
)(
5
-
3)
=
2(
5
-
3
)
2
=
5
-
3

方法二:

2
5
+
3
=
(
5
)2-(
3
)2
5
+
3
=
(
5
+
3
)(
5
-
3
)
5
+
3
=
5
-
3

(2)

1
3
+1
+
1
5
+
3
+
1
7
+
5
+…+
1
2n+1
+
2n-1

=

3
-1
2
+
5
-
3
2
+
7
-
5
2
+…+
2n+1
-
2n-1
2

=

(
3
-1)+(
5
-
3
)+(
7
-
5
)+…+(
2n+1
-
2n-1
)
2

=

3
-1+
5
-
3
+
7
-
5
+…+
2n+1
-
2n-1
2

=

2n+1
-1
2

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