Question

解方程x+1除以x+2+x+7除以x+8=x+5除以x+6+x+3除以x+4

Answer 1

(x+1)/(x+2)+(x+7)/(x+8)=(x+5)/(x+6)+(x+3)/(x+4)
1-1/(x+2)+1-1/(x+8)=1-1/(x+6)+1-1/(x+4)
1/(x+2)+1/(x+8)=1/(x+6)+1/(x+4)
1/(x+2)-1/(x+4)=1/(x+6)-1/(x+8)
2/(x+2)(x+4)=2/(x+6)(x+8)
(x+2)(x+4)=(x+6)(x+8)
x²+6x+8=x²+14x+48
-8x=40
x=-5
经检验，它是原方程的根。