Question

怎样解x-5分之一-x-6分之一=x-8分之一-x-9分之一这个方程

Answer 1

x-5分之一-x-6分之一=x-8分之一-x-9分之一
1/(x-5) +1/(x-9)=1/(x-8) +1/(x-6)
(x-9+x-5)/(x-5)(x-9)=(x-6+x-8)/(x-8)(x-6)
(2x-14)/(x^2-14x+45)=(2x-14)/(x^2-14x+48)
(2x-14)(x^2-14x+45)-(2x-14)(x^2-14x+48)=0
(2x-14)(x^2-14x+45-x^2+14x-48)=0
(2x-14)*3=0
2x-14=0
x=7

Answer 2

1/(x-5)-1/(x-6)=1/(x-8)-1/(x-9)
[(x-6)-(x-5)]/[(x-5)(x-6)]=[(x-9)-(x-8)]/[(x-8)(x-9)]
(-1)/[(x-5)(x-6)]=(-1)/[(x-8)(x-9)]
∴(x-5)(x-6)=(x-8)(x-9)
x²-11x+30=x²-17x+72
6x=42
x=7
经检验x=7是原方程的根