问题 解答题
(1)已知x=1+
2
,求代数式
x2+2x+1
x2-1
-
x
x-1
的值;
(2)解方程:
1
x-2
=
3
x
答案

(1)

x2+2x+1
x2-1
-
x
x-1

=

(x+1)2
(x+1)(x-1)
-
x
x-1

=

x+1
x-1
-
x
x-1

=

1
x-1

当x=1+

2
时,原式=
1
1+
2
-1
=
2
2

(2)

1
x-2
=
3
x

去分母,得3(x-2)=x

去括号、移项,得3x-x=6

合并,得2x=6

解得x=3,

经检验,x=3是原方程的解.

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