一道分式计算数学题,1/（x-10)+1/(x-6)=1/(x-7)+1/(x-9)
问题描述：
一道分式计算数学题,
1/（x-10)+1/(x-6)=1/(x-7)+1/(x-9)
答
1/(x-10)-1/(x-9)=1/(x-7)-1/(x-6)
1/(x-10)(x-9)=1/(x-7)(x-6)
(x-7)(x-6)=(x-10)(x-9)
x^2-13x+42=x^2-19x+90
6x=48
x=8
答
所以 1/(x-10)-1/(x-7)=1/(x-9)-1/(x-6)
通分可得 3/(x-10)(x-7)=3/(x-9)(x-6)
(x-10)(x-7)=(x-9)(x-6)
x^2-17x+70=x^2-15x+54
2x=16
x=8
答
1/[(x-10)(x-9)]=1/[(x-6)(x-7)]
(x-10)(x-9)=(x-6)(x-7)
-19x+90=-13x+42
6x=48
x=8