1/(x+2)-1/(x+4)=1/(x-6)-1/(x-4) 解方程啊。在线等

1. 1/(x+2)-1/(x+4)=1/(x-6)-1/(x-4) 解方程啊。在线等

1/(x+2)-1/(x+4)=1/(x-6)-1/(x-4)
1/(x+2)+1/(x-4)=1/(x-6)+1/(x+4)
(x+2+x-4)/(x+2)(x-4)=(x+4+x-6)/(x-6)(x+4)
(2x-2)/(x^2-2x-8)=(2x-2)/(x^2-2x-24)
因为x^2-2x-8不等于x^2-2x-24
而分子相等
所以分子=0
2x-2=0
x=1
检验，成立

2. 1/x-1-1/x-2=1/x-3-1/x-4

先在等式两边分别通分，得:
(x-2)-(x-1)
(x-4)-(x-3)
分数线------
=
------
(x-1)(x-2)
(x-3)(x-4)
-1
-1
------
=
------
(x-1)(x-2)
(x-3)(x-4)
(x-3)(x-4)
=
(x-1)(x-2)
x^2-7x+12
=
x^2-3x+2
-4x
=
-10
x
=
2.5
检验:当x=2.5时，x-1≠0、x-2≠0、x-3≠0、x-4≠0.
∴x=2.5是原分式方程的解。
(全手打，求楼主采纳!)

3. 1/x+1+2/x-1=4/x^2-1

1/(x+1)
+
2/(x-1)
=
4/(x²-1)
因为(x²-1)
=
(x-1)(x+1)
≠0，左右两端同乘(x²-1)
x
-
1
+
2(x
+
1)
=
4
3x
+
1
=
4
3x
=
3
x
=
1
检验,
x
=
1
使分母为0，不符合题意，所以原分式方程无解

4. 1.1/x+1/x+1=5/2x+2 解方程 2.24、x-17-x/x-1=1

第一题1/x+1/x+1=5/2x+2
等号后面2x+2的+2是包含在分母里的吗
还有第二题是x-17-x/x-1=1吗?
等号左边x-1的-1是不是包含在分母里的???
题目要写清楚```

5. 解方程:1-x/(x-2)=1/(2-x)-2

这是一个分式方程,所以第一步先去分母,方程两边同时乘以(x-2),原方程就可化为:
(x-2)-x=-1-2(x-2)，整理得:-2=-1-2x+4，解得x=5/2，经检验:x=5/2为原方程的解

6. 1/x²+x+1/x²+3x+2+1/x²+5x+6+1/x²+7x+12,分式方程，急急急！

原式=1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)

=1/x-1/(x+4)
=4/(x²+4x)

7. 1/x(x+3)+1/(x+3)(x+6)+1/(x+6)(x+9)=3/2x+18

1/x(x+3)+1/(x+3)(x+6)+1/(x+6)(x+9)=3/2x+18
1/x(x+3)+1/(x+3)(x+6)+1/(x+6)(x+9)
=[1/x-1/(x+3)+1/(x+3)-1/(x+6)+1(x+6)-1/(x+9)]/3
=[1/x-1/(x+9)]/3
=3/x(x+9)=3/2x+18
2x+18=x(x+9)
x²+7x-18=0
(x-2)(x+9)=0
x1=2
x2=-9(经检验知，不合舍去）
所以，x=2是原分式方程的解

8. x²-1=4(x+1)解方程

解：x²-1=4x+4
x²-4x-5=0
（x-5）（x+1）=0
x1=5，x2=-1