问题 填空题
分式方程2-
1
4-
3
6-
5
2-
1
4-
3
6-
5
x
=x的根是______.
答案

原方程化为

1
4-
3
6-
5
2-
1
4-
3
6-
5
x
=2-x,

∴4-

3
6-
5
2-
1
4-
3
6-
5
x
=
1
2-x
,即
3
6-
5
2-
1
4-
3
6-
5
x
=
7-4x
2-x

6-

5
2-
1
4-
3
6-
5
x
=
6-3x
7-4x
,即
5
2-
1
4-
3
6-
5
x
=
36-21x
7-4x

∴2-

1
4-
3
6-
5
x
=
35-20x
36-21x
,即
1
4-
3
6-
5
x
=
37-22x
36-21x

∴4-

3
6-
5
x
=
36-21x
37-22x
,即
3
6-
5
x
=
112-67x
37-22x

∴6-

5
x
=
111-66x
112-67x
,即
5
x
=6-1+
1-x
112-67x

整理,得

5(1-x)
x
-
1-x
112-67x
=0,

解得x1=1,x2=

5
3

经检验:x1=1,x2=

5
3
是原方程的根.

故答案为:x1=1,x2=

5
3

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