如何解3x-3/x-2+x-5/x-8=3x-9/x-4+x-3/x-6

题目

如何解3x-3/x-2+x-5/x-8=3x-9/x-4+x-3/x-6

答案

(3x-3)/(x-2)+(x-5)/(x-8)=(3x-9)/(x-4)+(x-3)/(x-6)
(3x-3)/(x-2)-(3x-9)/(x-4)=(x-3)/(x-6)-(x-5)/(x-8)
3[(x-1)/(x-2) -(x-3)/(x-4）]=(x-3)/(x-6)-(x-5)/(x-8)
左右同时通分得
3[(x-1)(x-4)-(x-3)(x-2)]/(x-2)(x-4)=[(x-3)(x-8)-(x-5)(x-6)]/(x-6)(x-8)
3（x²-5x+4-x²+5x-6)/(x-2)(x-4) =(x²-11x+24-x²+11x-30)/(x-6)(x-8)
3×（-2）/(x-2)(x-4)=（-6）/(x-6)(x-8)
1/(x-2)(x-4)=1/(x-6)(x-8)
(x-2)(x-4)=(x-6)(x-8)
x²-6x+8=x²-14x+48
-6x+14x=48-8
8x=40
x=5