Question

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

Answer 1

(x+2)/(x+1)-(x+4)/(x+3)=(x+6)/(x+5)-(x+8)/(x+7)
[(x+1)+1]/(x+1)-[(x+3)+1]/(x+3)=[(x+5)+1]/(x+5)-[(x+7)+1]/(x+7)
(x+1)/(x+1)+1/(x+1)-(x+3)/(x+3)-1/(x+3)=(x+5)/(x+5)+1/(x+5)-(x+7)/(x+7)-1/(x+7)
1+1/(x+1)-1-1/(x+3)=1+1/(x+5)-1-1/(x+7)
1/(x+1)-1/(x+3)=1/(x+5)-1/(x+7)
[(x+3)-(x+1)]/[(x+1)(x+3)]=[(x+7)-(x+5)]/[(x+5)(x+7)]
2/[(x+1)(x+3)]=2/[(x+5)(x+7)]
(x+1)(x+3)=(x+5)(x+7)
x²+4x+3=x²+12x+35
4x-12x=35-3
-8x=32
x=-4
经检验 x=-4是原方程的根