(x-10)/(x-11)+(x-16)/(x-17)=(x-12)/(x-13)+(x-14)/(x-15)快,急用
问题描述：
(x-10)/(x-11)+(x-16)/(x-17)=(x-12)/(x-13)+(x-14)/(x-15)
快,急用
答
答：
(x-10)/(x-11)+(x-16)/(x-17)=(x-12)/(x-13)+(x-14)/(x-15)
1+1/(x-11)+1+1/(x-17)=1+1/(x-13)+1+1/(x-15)
1/(x-11)+1/(x-17)=1/(x-13)+1/(x-15)
(x-17+x-11)/[(x-11)(x-17)]=(x-15+x-13)/[(x-13)(x-15)]
(2x-28)/[(x-11)(x-17)]=(2x-28)/[(x-13)(x-15)]
所以：
2x-28=0或者(x-11)(x-17)=(x-13)(x-15)（无解）
所以：x=14
经检验，x=14是原分式方程的根
答
两边减去2
(x-10)/(x-11)-1+(x-16)/(x-17)-1=(x-12)/(x-13)-1+(x-14)/(x-15)-1
1/(x-11)+1/(x-17)=1/(x-13)+1/(x-15)
(2x-28)/(x-11)(x-17)-(2x-28)/(x-13)(x-15)=0
(2x-28)[1/(x²-28x+187)-1/(x²-28x+195)=0
因为x²-28x+187≠x²-28x+195
所以2x-28=0
x=14