（X²-X-5）/X+2=（X+2）+1/（X+2）-5是如何化简的来的,

moneyowner2022-10-04 11:39:542条回答

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kagensea 共回答了20个问题 | 采纳率70%: (X²-X-5）/(X+2)
=[(x^2+4x+4)-(5x+10)+1]/(x+2)
=[(x+2)^2-5(x+2)+1]/(x+2)
=(x+2)+1/(x+2)-5; 1年前

summer_kiss 共回答了5个问题 | 采纳率: (X²-X-5）/X+2)
=[(X²-4)-(X+1）]/X+2)
=(X²-4)/(X+2)-(X+1）/(X+2)
=X-2-(X+2-1)/(X+2)
=X-2-1+1/(X+2)
=X+2-5+1/（X+2）-5
=（X+2）+1/（X+2）-5; 1年前

1/（x+1）（x+2）+1/（x+2）（x+3）+…+1/（x+99）（x+100） 世上第一丑男1年前1: 娟娟925 共回答了16个问题 | 采纳率93.8%

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+99)(x+100)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+.+1/(x+99)-1/(x+100)
=1/x-1/(x+100)
=100/[x(x+100)]

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1/（X+1)(X+2）+1/(X+2))(X+3)+...+1/(X+2005)(X+2006)=1/2X+4012 旋转的木马991年前3: 轮日共回答了16个问题 | 采纳率87.5%

1/（X+1)(X+2）+1/(X+2))(X+3)+...+1/(X+2005)(X+2006)=1/2X+4012
1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+...+1/(x+2005)-1/(x+2006)=1/2(x+2006)
1/(x+1)-1/(x+2006)=(1/2)*1/(x+2006)
1/(x+1)=(3/2)*1/(x+2006)
3(x+1)=2(x+2006)
x=4012-3
x=4009

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解方程:1/x（x+2）+1/（x+1）（x+3）+…+1/（x+8）（x+10）=0 众网友1年前2: yiguo765 共回答了15个问题 | 采纳率100%

1/2*[1/x-1/(x+2)]+1/2*[1/(x+1)-1/(x+3)]+…+1/2*[1/(x+8)-1/(x+10)]=0
1/2*[1/x-1/(x+2)+1/(x+1)-1/(x+3)+1/(x+2)-1/(x+4)+…+1/(x+8)-1/(x+10)]=0
1/2*[1/x+1/(x+1)-1/(x+9)-1/(x+10)]=0
所以1/x+1/(x+1)-1/(x+9)-1/(x+10)=0
[1/x-1/(x+9)]+[1/(x+1)-1/(x+10)]=0
9/[x(x+9)]+9/[(x+1)(x+10)]=0
9/[x(x+9)]=-9/[(x+1)(x+10)]
所以x(x+9)=-(x+1)(x+10)
x^2+9x=-(x^2+11x+10)
x^2+9x+x^2+11x+10=0
2x^2+20x+10=0
x^2+10x+5=0
x=-5±2√5
打字不易,

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1/（X+2）+1/(X+5)=1/（X+3）+1/（X+4）江湖救急,方程求解! 一剑红飘1年前3: leonzhang 共回答了15个问题 | 采纳率80%

1/（X+2）+1/(X+5)=1/（X+3）+1/（X+4）移项
1/（X+2）-1/(X+3)=1/（X+4）-1/（X+5）
左右分别通分得（X+2）（X+3）=（X+4）（X+5）
展开后得4x=-14 所以x=-7/2

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