一些常见的数学题

1/(x^2-y^2)+2/(x-y)^2
=1/(x+y)(x-y)+2/(x-y)^2
=(x-y+2(x+y))/(x+y)(x-y)^2
=(3x+y)/(x+y)(x-y)^2
1.
x/(x-3)-2=-3/(3-x)
x/(x-3)-3/(x-3)-2=0
-2=0无解
2.
(x+1)(x-1)+2(x-1)^2=0
(x-1)(x+1+2x-2)=0
(x-1)(3x-1)=0
x=1,1/3
又x-1不为0
则x=1/3
3.
(5x-1)^2-(3x-2)^2=0
(5x-1-(3x-2))(5x-1+3x-2)=0
(2x+1)(8x-3)=0
x=-1/2,3/8
4.
7x^2+2x=0
x(7x+2)=0
x=0,-2/7
5.
(2x-5)^2-x^2=0
(2x-5-x)(2x-5+x)=0
(x-5)(3x-5)=0
x=5,3/5

x^2/25-y^2/16
=(x/5-y/4)(x/5+y/4)

计算：
1/(x^2-y^2)+2/(x-y)^2
=1/[(x+y)(x-y)]+2/(x-y)^2
=(x-y)/[(x+y)(x-y)^2]+2(x+y)/[(x+y)(x-y)^2]
=(x-y+2x+2y)/[(x+y)(x-y)^2]
=(3x+y)/[(x+y)(x-y)^2]

解方程：
1.
x/(x-3)-2=(-3)/(3-x)
(x-3)/(x-3)=2
1=2
方程错了。。。

2.
(x+1)/(x^2-2x+1)+2/(x-1)=0
(x+1)/(x-1)^2+2/(x-1)=0
(x+1)+2(x-1)=0
x+1+2x-2=0
3x=1
x=1/3

3.