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解方程(x+1/x+2)+(x+8/x+9)=(x+2/x+3)+(x+7/x+8) 注:要求用简便...

1、移项得(x+1)/(x+2)-(x+2)/(x+3)=(x+7)/(x+8)-(x+8)/(x+9)2、化简原式(x+1)/(x+2)=(x+2-1)/(x+2)=1-1/(x+2)(x+2)/(x+3)=(x+3-1)/(x+3)=1-1/(x+3)(x+7)/(x+8)=(x+8-1)/(x+8)=1-1/(x+8)(x+8)/(x+9)=(x+9-1)/(x+9)=1-1/(x+9)所以,原式=1/(x

x+1/x+2+x+8/x+9=x+2/x+3+x+7/x+8 题是这样的吧(x+1)/(x+2)+(x+8)/x+9)=(x+2)/(x+3)+(x+7)/(x+8)先把每一个提一个1出来1/(x+2)-1 +1/(x+9)-1=1/(x+3)-1 +1/(x+8)-1约去1得 1/(x+2)+1/(x+9)=1/(x+3)+1/(x+8) 展开 作业帮用户 2017-10-28 举报

1/x(x+1)+1/(x+1)(x+2)1/(x+8)(x+9)=(2x+3)/x(x+9) (1/x-1/x+1)+(1/x+1-1/x+2)++1/x+8-1/x+9=(2x+3)/x(x+9) 1/x-1/x+9=(2x+3)/x(x+9) 9/x(x+9)=(2x+3)/x(x+9) 2x+3=9 x=3

(x+1)/(x+2)+(x+6)/(x+7)=(x+2)/(x+3)+(x+5)/(x+6)1-1/(x+2)+1-1/(x+7)=1-1/(x+3)+1-1/(x+6)-1/(x+2)-1/(x+7)=-1/(x+3)-1/(x+6)1/(x+2)+1/(x+7)=1/(x+3)+1/(x+6)1/(x+2)-1/(x+3)=1/(x+6)-1/(x+7)(x+3-(x+2))/(x+2)(x+3)=(x+7-(x+6))/(x+6)(x+7)1/(x+2)(x+3)=1/(x+6)(x+7)(x+2)(x+3)=(x+6)(x+7)x^2+5x+6=x^2+13x+428x=-36x=-9/2

(X+1/X+2)-(X+2/X+3)=(X+5/X+6)-(X+6/X+7)(X方+4X+3-X方-4X-4)/(X方+5X+6)=(X方+12X+35-X方-12X-36)/(X方+13X+42)X方+5X+6=X方+13X+42-8X=36X=-9/2

(X+1)/(X+2)+(X+7)/(X+8)=(X+2)/(X+3)+(X+8)/(X+9)1-1/(X+2) + 1-1/(X+8)=1-1/(X+3) + 1- 1/(X+9)所以1/(X+2) + 1/(X+8)=1/(X+3) + 1/(X+9),移项,1/(X+2) - 1/(X+3) =1/(X+9) - 1/(X+8)通分,[(X+3)-(X+2)]/[(X+2)(X+3)] = [(X+8) - (X+9)]/[(X+9)(X+8)]所

x+1/x+2+x+6/x+7=x+2/x+3+x+5/x+61-1/(x+2)+1-1/(x+7)=1-1/(x+3)+1-1/(x+6)1/(x+6)-1/(x+7)=1/(x+2)-1/(x+3)1/(x+6)(x+7)=1/(x+2)(x+3)(x+6)(x+7)=(x+2)(x+3)13x+42=5x+68x=-36x=-4.5经检验x=-4.5是方程的根.

原方程变形为:x+1x+2-x+2x+3=x+7x+8-x+8x+9,去分母,得(x+2)(x+3)=(x+8)(x+9),整理,得12x+66=0,解得 x=-5.5,经检验,x=-5.5是原方程的解.故答案为:-5.5.

这道题有问题吧,没有解啊,方程两面的常数和都是9,原题写错了吧

(X+1/X+2)+(X+2/X+3)=(X+3/X+4)+(X+4/ X+5) [(x+2)-1]/(x+2)+[(x+3)-1]/(x+3)=1-1/(x+4)+1-1/(x+5) (后面我偷懒了) 1/(x+2)+1/(x+3)=1/(x+4)+1/(x+5) 1/(x+2)-1/(x+4)=1/(x+3)-1/(x+5) 1/(x+2)(x+4)=1/(x+3)(x+5) (x+2)(x+4)=-(x+3)(x+5) x^2+6x+8=-x^2-8x-15 2x^2+14x+23=0 x=[-14±√(196-184)]/4=(-7±√3)/2 经检验,x=(-7±√3)/2是原方程的根!

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