1、4X/(X²-4)=A/(X+2）+B/(X-2)
=[A(X-2)+B(X+2)]/(X+2)(X-2)
=[(A+B)x+2(B-A)]/(X+2)(X-2)
A+B=4
2(B-A)=0
A=2 B=2
B²+A²＝2²+2²=8
2、1/x-1/y=3
y-x=3xy x-y=-3xy
( 2x+3xy-2y)/(x-2xy-y)=[2(x-y)+3xy]/(x-y)-2xy
=(-6xy+3xy)/(-3xy-2xy)
=-3xy/-5xy
=3/5
3、x²+3x+1=0
x+3+1/x=0
x+1/x=-3
X²+1/X²=(x+1/x)²-2
=(-3)²-2
=7
4、1/(x-5)-1/(x-6) =1/(x-8)-1/(x-9)
[(x-6)-(x-5)]/(x-5)(x-6)=[(x-9)-(x-8)]/(x-8)(x-9)
-1/(x-5)(x-6)=-1/(x-8)(x-9)
(x-5)(x-6)=(x-8)(x-9)
x²-11x+30=x²-17x+72
6x=42
x=7
检验：略
4(3X-1)/（2X-2）-(2X)/(3X-3)=1/2
4(3X-1) /2(X-1)-(2X)/3(X-1)=1/2
12(3X-1)-4x=3(x-1）
36x-12-4x=3x-3
29x=9
x=9/29
检验：略