Question

解方程：(x-4)/(x-5)-(x-5)/(x-6)=(x-7)/(x-8)-(x-8)/(x-9)

Answer 1

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

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

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

通分：

-1/[（x-5）(x-6)]=-1/[（x-8）(x-9)]

（x-5）(x-6)=（x-8）(x-9)

x^2-11x+30=x^2-17x+72

6x=42

x=7