解方程：x-7分之1-x-5分之1=x-6分之1-x-4分之1能告诉下方法么?

Question

解方程：x-7分之1-x-5分之1=x-6分之1-x-4分之1 能告诉下方法么?

Answer 1

1/(x-7)-1/(x-5)=1/(x-6)-1/(x-4)
1/(x-6)-1/(x-7)=1/(x-4)-1/(x-5)
(x-7)/(x-6)(x-7)-(x-6)/(x-6)(x-7)=(x-5)/(x-4)(x-5)-(x-4)/(x-4)(x-5)
[(x-7)-(x-6)]/(x-6)(x-7)=[(x-5)-(x-4)]/(x-4)(x-5)
(x-7-x+6)/(x-6)(x-7)=(x-5-x+4)/(x-4)(x-5)
-1/(x-6)(x-7)=-1/(x-4)(x-5)
1/(x-6)(x-7)=1/(x-4)(x-5)
(x-6)(x-7)=(x-4)(x-5)
x^2-13x+42=x^2-9x+20
13x-9x=42-20
4x=22
x=11/2
经检验x=11/2是方程有解