题目

解方程：(x-4)/(x-5)-(x-5)/(x-6)=(x-7)/(x-8)-(x-8)/(x-9)、、x=?

提问时间：2020-10-08

答案

(x-4)/(x-5) -(x-5)/(x-6)=(x-7)/(x-8)-(x-8)/(x-9)
(x-4)/(x-5)+(x-8)/(x-9)=(x-5)/(x-6)+(x-7)/(x-8)
(x-5+1)/(x-5)+(x-9+1)/(x-9)=(x-6+1)/(x-6)+(x-8+1)/(x-8)
1/(x-5)+1/(x-9) +2=1/(x-6) +1/(x-8)+2
1/(x-5)+1/(x-9)=1/(x-6)+1/(x-8)
[(x-5)+(x-9)]/[(x-5)(x-9)]=[(x-6)+(x-8)]/[(x-6)(x-8)]
(2x-14)/(x²-14x+45)=(2x-14)/(x²-14x+48)
分母x²-14x+45恒≠x²-14x+48,要等式成立,只有分子=0
2x-14=0
x=7
代入分式方程检验,分母均≠0,x=7是分式方程的解.
x=7