Question

★★★（初二）超级难的竞赛数学题

(5x-96)/(x-19)+(x-8)/(x-9)=(4x-19)/(x-6)+(2x-21)/(x-8)
求x的值

好难啊~~~~
老师给了一点提示，我还记得：
好像什么拆分、分步运算

各位，就谢谢了~~~！~！~~

Answer 1

(5x-96)/(x-19)+(x-8)/(x-9)=(4x-19)/(x-6)+(2x-21)/(x-8)
=>5+(-1)/(x-19)+1+(1)/(x-9)=4+(5)/(x-6)+2+(-5)/(x-8) -------拆分
=>(-1)/(x-19)+(1)/(x-9)=(5)/(x-6)+(-5)/(x-8) ---------------分步运算
=>(-10)/(x-19)(x-9)=(5)(-2)/(x-6)(x-8)
=>(x-19)(x-9)=(x-6)(x-8)
=>x^2-28x+19*9=x^2-14x+6*8
=>14x=123
x=123/14

Answer 2

原等式等价于：
5-1/(x-19)+1+1/(x-9)=4+5/(x-6)+2-5/(x-8)
-1/(x-19)+1/(x-9)=5/(x-6)-5/(x-8)
等价于：
1/(x-9)(x-19)=1/(x-6)(x-8)
接着就很容易了