Question

讨论方程的解法：x-2分之x-3+x-3分之x-4=x-4分之x-5+x-1分之x-2

Answer 1

解：
(x-3)/(x-2)+(x-4)/(x-3)=(x-5)/(x-4)+(x-2)/(x-1)
(x-3)/(x-2)-(x-5)/(x-4)=(x-2)/(x-1)-(x-4)/(x-3)
[(x-3)(x-4)-(x-5)(x-2)]/[(x-2)(x-4)]=[(x-2)(x-3)-(x-4)(x-1)]/[(x-1)(x-3)]
[(x²-7x+12)-(x²-7x+10)]/(x²-6x+8)=[(x²-5x+6)-(x²-5x+4)]/(x²-4x+3)
2/(x²-6x+8)=2/(x²-4x+3)
2(x²-6x+8)=2(x²-4x+3)
x²-6x+8=x²-4x+3
x²-6x-x²+4x=3-8
-2x=-5
x=5/2

Answer 2

(x-3)/(x-2)+(x-4)/(x-3)=(x-5)/(x-4)+(x-2)/(x-1)
(x-3)/(x-2)-(x-5)/(x-4)=(x-2)/(x-1)-(x-4)/(x-3)
[(x-3)(x-4)-(x-5)(x-2)]/[(x-2)(x-4)]=[(x-2)(x-3)-(x-4)(x-1)]/[(x-1)(x-3)]
[(x²-7x+12)-(x²-7x+10)]/(x²-6x+8)=[(x²-5x+6)-(x²-5x+4)]/(x²-4x+3)
2/(x²-6x+8)=2/(x²-4x+3)
2(x²-6x+8)=2(x²-4x+3)
x²-6x+8=x²-4x+3
x²-6x-x²+4x=3-8
-2x=-5
x=5/2