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