1/(x^2+7x)-1/(x^2+7x+6)+1/(x^2+7x+18)-1/(x^2+7x+12)=0
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1/(x^2+7x)-1/(x^2+7x+6)+1/(x^2+7x+18)-1/(x^2+7x+12)=0
1/(x^2+7x)-1/(x^2+7x+6)+1/(x^2+7x+18)-1/(x^2+7x+12)=0
1/(x^2+7x)-1/(x^2+7x+6)+1/(x^2+7x+18)-1/(x^2+7x+12)=0
设y=x^2+7x+6
原方程化为1/(y-6)-1/y+1/(y+12)-1/(y+6)=0
12/(y^2-36)-12/(y^2+12y)=0
1/(y^2-36)=1/(y^2+12y)
y^2-36=y^2+12y
12y=-36
y=-3
x^2+7x+6=-3
x^2+7x+9=0
x=-7/2±1/2√13
经检验x=-7/2±1/2√13是原方程的解
1/(x^2+7x)-1/(x^2+7x+6)+1/(x^2+7x+18)-1/(x^2+7x+12)=0
令 x^2+7x=t
则上式变为
1/t-1/(t+6)+1/(t+18)-1/(t+12)=0
1/t+1/(t+18)= 1/(t+6)
+1/(t+12)
(t+t+18)/t(t+18)= (t+12+t+6)/(t+6)(t+12...
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1/(x^2+7x)-1/(x^2+7x+6)+1/(x^2+7x+18)-1/(x^2+7x+12)=0
令 x^2+7x=t
则上式变为
1/t-1/(t+6)+1/(t+18)-1/(t+12)=0
1/t+1/(t+18)= 1/(t+6)
+1/(t+12)
(t+t+18)/t(t+18)= (t+12+t+6)/(t+6)(t+12)
(t+9)/t(t+18)= (t+9)/(t+6)(t+12)
(t+9)t(t+18)- (t+9)(t+6)(t+12)=0
(t+9)(t^2+18t-t^2-12t-6t+72)=0
(t+9)=0
t=-9
x^2+7x=-9
x^2+7x+9=0
x=(-7+√49-4*1*9)/2= (-7+√13)/2
或 x=(-7-√49-4*1*9)/2= (-7-√13)/2
经验证x=
(-7+√13)/2或 x=
(-7-√13)/2 都是方程的解
收起
令x^2+7x=y
原式=1/y-1/(y+6)+1/(y+18)-1/(y+12)
=6/y(y+6)-6/(y+18)(y+12)=0
有：y(y+6)=(y+18)(y+12)
解得:y=-9
所以x^2+7x=-9
x=-7/2±√13/2