解方程 x+2/x+1+x+8/x+7=x+6/x+5+x+4/x+3

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

解方程 x+2/x+1+x+8/x+7=x+6/x+5+x+4/x+3
首先由题意得x+1≠0,x+7≠0,x+5≠0,x+3≠0,
即x≠-1,x≠-7,x≠-5,x≠-3,则先简化方程
(x+1+1)/(x+1)+(x+7+1)/(x+7)=(x+5+1)/(x+5)+(x+3+1)/(x+3)
即1+1/(x+1)+1+1/(x+7)=1+1/(x+5)+1+1/(x+3)
1/(x+1)+1/(x+7)=1/(x+5)+1/(x+3)
1/(x+1)-1/(x+3)=1/(x+5)-1/(x+7) 两边通分可得
[(x+3)-(x+1)]/[(x+3)(x+1)]=[(x+7)-(x+5)]/[(x+7)(x+5)]
即2/[(x+3)(x+1)]=2/[(x+7)(x+5)]
∴(x+3)(x+1)=(x+7)(x+5)
x²+4x+3=x²+12x+35
4x+3=12x+35
x=-4
经检验,x=-4是原方程的解!

(x+2)/(X+1)-1+(x+8)/(x+7)-1=(x+6)/(x+5)-1+(x+4)/(x+3)-1
1/(x+1)+1/(x+7)=1/(x+5)+1/(x+3)
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^2+4x+3)=2/(x^2+12x+35)
x^2+4x+3=x^2+12x+35
4x+3=12x+35
x=-4