Question

解方程:1/(x-5)-1/(x-6)=1/(x-8)-1/(x-9)

Answer 1

(x-4)/(x-5)+(x-8)/(x-9)=(x-7)/(x-8)+(x-5)/(x-6)

(x-5+1)/(x-5)+(x-9+1)/(x-9)=(x-8+1)/(x-8)+(x-6+1)/(x-6)

1+1/(x-5)+1+1/(x-9)=1+1/(x-8)+1+1/(x-6)

1/(x-5)+1/(x-9)=1/(x-8)+1/(x-6)

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)

-11x+30=-17x+72

6x=42

x=7

经检验是原方程的根.