一道分式方程 要解法

题目

一道分式方程 要解法
x-5分之x-4 + x-1分之3 = x平方-1分之6
x-5分之x-4 + x-1分之3 =x-8分之x-7 - x-9分之x-8= x-5分之x-4

答案

（x-4）(x+1)(x-1)/(x-5）(x+1)(x-1) +3(x-5)(x+1)/(x-5）(x+1)(x-1) =6(x-5)/(x-5）(x+1)(x-1)
（x-4）(x+1)(x-1)/(x-5）(x+1)(x-1) +3(x-5)(x+1)/(x-5）(x+1)(x-1)-6(x-5)/(x-5）(x+1)(x-1)=0
（x-4）(x+1)(x-1)+3(x-5)(x+1)-6(x-5)/(x-5）(x+1)(x-1)=0
（x-4）(x+1)(x-1)+3(x-5)(x+1)-6(x-5)=0
（x-4）(x+1)(x-1)+3(x-5)(x+1)=6(x-5)
(x+1)（x2-4x-x+4+3x-15)=6x-30
(x+1)（x2-2x-11)=6x-30
(x+1)（x2-2x+1-12)=6x-30
(x+1）(x-1)2-12x-12=6x-30
(x+1）(x-1)2=18(x-1)
(x+1）(x-1)=18
x2-1=18
x2=19
x=正负根号19