解方程x-6分之x-5+x-9分之x-8=x-8分之x-7+x-7分之x-6

Question

解方程x-6分之x-5+x-9分之x-8=x-8分之x-7+x-7分之x-6

Answer 1

(x-5)/(x-6)+(x-8)/(x-9)=(x-7)/(x-8)+(x-6)/(x-7)
(x-5)/(x-6)-(x-6)/(x-7)=(x-7)/(x-8)-(x-8)/(x-9)
[(x-5)(x-7)-(x-6)²/[(x-6)(x-7)]=[(x-7)(x-9)-(x-8)²]/[(x-8)(x-9)]
(x²-12x+35-x²+12x-36)/[(x-6)(x-7)]=(x²-16x+63-x²+16x-64)/[(x-8)(x-9)]
-1/[(x-6)(x-7)]=-1/[(x-8)(x-9)]
(x-6)(x-7)=(x-8)(x-9)
x²-13x+42=x²-17x+72
17x-13x=72-42
4x=30
x=7.5
经检验x=7.5是原方程的根.