Question

解方程：x-4/x-5 ➕x-8/x-9=x-5/x-6➕x-7/x-8

Answer 1

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

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

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

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

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

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

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

x²-17x+72=x²-11x+30

-6x=-42

x=7

经检验x=7是原方程的解