1/x(x+1)+1/(x+1)(x+2)+...+1/(x+999)(x+1000)=?

计算1/x(x+1)+1/(x+1)(x+2)…+1/(x+1998)(x+1999)

huimou19731年前1

不可琢磨的 共回答了16个问题 | 采纳率100%

这到题得用到一个公式1/x(x+1)=1/x-1/(x+1)
所以原式等于1/x-1/(x+1)+1/(x+1)-1/(x+2)+.+1/(x+1998)-1/(x+1999)
正,负向抵消得1/x-1/(x+1999)
原式=1/x-1/(x+1999)

1年前查看全部

要用二阶导数证该题,求教!已知函数f(x)=(ln(x))/(x+1)+1/x证：当x>0且x不等于1时,f(x)>(l

要用二阶导数证该题,求教!
已知函数f(x)=(ln(x))/(x+1)+1/x
证：当x>0且x不等于1时,f(x)>(ln(x))/(x-1)

永远忘记ww1年前1

bxs20007 共回答了10个问题 | 采纳率90%

1年前查看全部

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+……+1/(x+2007

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+……+1/(x+2007)(x+2008)求当X=1时,该式的值
请给出准确步骤

小白兔亚么白又白1年前7

ljbdoit 共回答了12个问题 | 采纳率100%

1/x(x+1)=1/x-1/(x+1)
1/(x+1)(x+2)=1/(x+1)-1/(x+2)
.
.
1/(x+2007)(x+2008)=1/(x+2007)-1/(x+2008)
所有式子相加得,右边两两相消
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+……+1/(x+2007)(x+2008)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+2007)-1/(x+2008)
=1/x-1/(x+2008)
=1/1-1/2009
=2008/2009

1年前查看全部

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+2004)(x+2005)

wcpoaiui1年前1

极光精灵 共回答了21个问题 | 采纳率85.7%

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+2004)(x+2005)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+-----+(1/(x+2004)-1/(x+2005)
=1/x-1/(x+2005)
=2005/(x^2+2005x)
用裂项相消法
1/（x+n)(x+n+1)=1/(x+n)-1/(x+n+1)

1年前查看全部

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+999)(x+1000)

yingguo07681年前3

dql_dql 共回答了17个问题 | 采纳率94.1%

1/x(x+1)=1/x-1/(x+1)
1/(x+1)(x+2)=1/(x+1)-1/(x+2)
...
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+999)(x+1000)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+999)-1/(x+1000)
=1/x-1/(x+1000)=1000/x(x+1000)

1年前查看全部

1/x(x-1)+1/x(x+1)+1/(x+1)(x+20.+1/(x+9)(x+10)=11/12

1/x(x-1)+1/x(x+1)+1/(x+1)(x+20.+1/(x+9)(x+10)=11/12
知道的回答!

yur20041年前1

CHHDRMR10000 共回答了13个问题 | 采纳率100%

原式=1/[x-1]-1/x+1/x-1/[x+1]+1/[x+1]-1/[x+2]+...+1/[x+9]-1/[x+10]=11/12
1/[x-1]-1/[x+10]=11/12
11/[x-1][x+10]=11/12
[x-1][x+10]=12
x=2或x= -11

1年前查看全部

1/(x+1)+1/(x+2)=1/x+1/(x+3)

Robotics1年前2

glwsm 共回答了16个问题 | 采纳率87.5%

1/(x+1)+1/(x+2)=1/x+1/(x+3)
1/(x+2)-1/(x+3)=1/x-1/(x+1)
[(x+3)-(x+2)]/[(x+2)(x+3)]=[(x+1)-x]/[x(x+1)]
1/[(x+2)(x+3)]=1/[x(x+1)]
x(x+1)=(x+2)(x+3)
x^2+x=x^2+5x+6
x-5x=6
-4x=6
x=-1.5
经检验x=-1.5是原方程的解

1年前查看全部

一、化简1/x(x+1)+1/(x+1)(x+2)+···+1/(x+2010)(x+2011)并求当x=1时该代数式的

一、化简1/x(x+1)+1/(x+1)(x+2)+···+1/(x+2010)(x+2011)并求当x=1时该代数式的值ps：这是应用题,要有过程please,
二、填空题：计算：1/1*2+1/2*3+1/3*4+···1/99*100=?
三、应用题：分式4x-5/2x的平方+x-6是两个分式m/x+2与n/2x-3相加得到的,求m,n的值

baiyue09191年前2

ztq1987 共回答了16个问题 | 采纳率87.5%

原式＝1/x-1/(x+1)+1/(x+1)-1/(x+2)+---+1/(x+2010)-1/(x+2011)=1/x-1/(x+2011)=1-1/2012
=2011/2012；
原式＝1-1/2+1/2-1/3+1/3-1/4+---+1/99-1/100=1-1/100=99/100；
（4x-5）/(2x^2+x-6)=m/(x+2)+n/(2x-3)
因为等式左边＝（4x-5）/(2x-3)(x+2),等式右边＝[m(2x-3)+n(x+2)]/(2x-3)(x+2)
所以：4x-5=2mx-3m+nx+2n=x(2m+n)+(2n-3m)
则：1式：2m+n=4,2式：2n-3m=-5
最后解得m=13/7,n=2/7；

1年前查看全部

解方程:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+9)(x+10)=5/1

解方程:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+9)(x+10)=5/12 急

78651431年前4

ZHT1201 共回答了22个问题 | 采纳率95.5%

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+9)(x+10)=5/12
1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+...+1/(x+9)-1/(x+10)=5/12
1/x-1/(x+10)=5/12
10/x(x+10)=5/12
所以x²+10x-24=0
(x+12)(x-2)=0
x=-12,x=2
经检验,x=-12和x=2是方程的解

1年前查看全部

已知1/1×2=1-1/2,1/2×3=1/2-1/3,1/3×4=1/3-1/4.,则1/x(x+1)+1/(x+1)

已知1/1×2=1-1/2,1/2×3=1/2-1/3,1/3×4=1/3-1/4.,则1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)

aqzv1年前3

snoopy85 共回答了17个问题 | 采纳率100%

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

1年前查看全部

解方程-1/X(X+1)+1/(X+1)(X+2)+.+1/(X+2009)(X+2010)+1/x+2010=2010

解方程-1/X(X+1)+1/(X+1)(X+2)+.+1/(X+2009)(X+2010)+1/x+2010=2010
解方程-1/X(X+1)+1/(X+1)(X+2)+.....+1/(X+2009)(X+2010)+1/(x+2010)=2010

jianjianmok1年前1

171m7ez 共回答了18个问题 | 采纳率88.9%

首先：1/x(x+1)=1/x-1/(x+1)
用这种方法可将方程左边化简为1/x-1/(x+1)+1/(x+1)-1/(x+2)+……-1/(x+2010)+1/(x+2010),也就是1/x
即1/x=2010,x=1/2010
第一项是负的么?如果是负的就得出2/(x+1)-1/x=2010,还是比较好做的

1年前查看全部

化简：1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+8)(x+9)

霍夫蔓1年前2

jdyb 共回答了24个问题 | 采纳率87.5%

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

1年前查看全部

化简:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+2013)(x+2014)

脑波控制1年前1

lizhangpeng 共回答了21个问题 | 采纳率71.4%

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+2013)(x+2014)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+.+1/(x+2013)-1/(x+2014)
=1/x-1/(x+2014)
=2014/x(x+2014)

1年前查看全部

数学问题：化简1/x(x+1)+1/(x+1)(x+2)+……+1/(x+2012)(x+2013),并求当x=1时该代

数学问题：化简1/x(x+1)+1/(x+1)(x+2)+……+1/(x+2012)(x+2013),并求当x=1时该代数式的值.

zzx3044151年前1

木梯子 共回答了19个问题 | 采纳率78.9%

分开,例1/x(x+1)=1/x-1/(x+1),依次下去最后只剩两项：1/x-1/(x+2013)

1年前查看全部

1/X(X+1)+1/(X+1)(X+2)+1/(X+2)(X+3)其中X的平方+3X+1=0

solky1年前1

xb0431 共回答了20个问题 | 采纳率95%

第一题
由X^2+3X+1=0,得X^2=-3X-1代入,
1/(X+1)(X+2)=1,故原式=1/X(X+1)+1+1/(X+2)(X+3)=
1+1/(-1-2X）+1/(2X+5)通分,原式=1+4/-(2X+5)(2X+1)=
1+4/-[4(X^2+3X+1)+1]=1-4=-3
第二题
移项,1/(x-10)-1/(x-7)=1/(x-9)-1/(x-6),通分得
3/(x^2-17x+70)=3/(x^2-15x+54),即(x^2-17x+70)=(x^2-15x+54),
得x=8

1年前查看全部

化简求值:1/x(x+1)+1/(x+)(x+2)+.1/(x+2005)(x+2006),其中X=1.

吉聿王1年前5

潇湘绝 共回答了13个问题 | 采纳率92.3%

1/x(x+1)+1/(x+)(x+2)+.1/(x+2005)(x+2006)
=1/x-1/(x+1)+1/(x+1)-1/(x+1)+...+1/(x+2005)-1/(x+2006)
=1-1/(x+2006)
=(x+2005)/(x+2006)
当x=1时
原式=2006/2007

1年前查看全部

计算:1/x(x+1)+1/(x+1)(x+2)+……+1/(x+2007)(x+2008).

chenddmarshal1年前3

小城故事0403 共回答了18个问题 | 采纳率88.9%

原式可等价于1/X-1/(X+1)+1/(X+1)-1/(X+2)+.+1/(X+2007)-1/(X+2008)=1/X-1/(X+2008)=X/(X(X+2008））

1年前查看全部

1/(x-1)(x+1)+1/(x+1)(x+3)+1/(x+3)(x+5)+1/(x+5)(x+7)+1/(x+7)(

1/(x-1)(x+1)+1/(x+1)(x+3)+1/(x+3)(x+5)+1/(x+5)(x+7)+1/(x+7)(x+9)+1/(x+9)(x+11)
x=√3-5
化简求值

cfahydt1年前2

ef_s2_5cclx0f9_9 共回答了25个问题 | 采纳率92%

1/(x-1)(x+1)+1/(x+1)(x+3)+1/(x+3)(x+5)+1/(x+5)(x+7)+1/(x+7)(x+9)+1/(x+9)(x+11)
=(1/2)×[1/(x-1)-1/(x+1)+1/(x+1)-1/(x+3)+1/(x+3)-1/(x+5)+1/(x+5)-1/(x+7)+1/(x+7)-1/(x+9)+1/(x+9)-1/(x+11)]
=(1/2)×(1/(x-1)-1/(x+11)]
=(1/2)×(x+11-x+1)/[(x-1)(x+11)]
=6/[(x-1)(x+11)]
=6/[(√3-6)(√3+6)]
=6/(3-36)
=-6/33
=-2/11

1年前查看全部

分式化简：（1）1/x-1/(X+1) (2)1/x(x+1)+1/(X+1)(x+2)+...+1/（x+999)(x

分式化简：（1）1/x-1/(X+1) (2)1/x(x+1)+1/(X+1)(x+2)+...+1/（x+999)(x+1000)

royfeng_1年前1

yaunfd 共回答了28个问题 | 采纳率92.9%

（1）1/x-1/(x+1)=（x+1-x）/（x（x+1））=1/(x(x+1))
(2)1/x(x+1)+1/(X+1)(x+2)+...+1/（x+999)(x+1000)
=1/x-1/(x+1）+1/(x+1)-1/(x+2)+……+1/(x+999)-1/(x+1000)
=1/x-1/(x+1000)
=(x+1000-x)/(x(x+1000))
=1000/(x(x+1000))

1年前查看全部

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+1/(x+4)(x+5)

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+1/(x+4)(x+5)=5/x^2+11x-708

мe℡恬1年前2

zhy3166 共回答了17个问题 | 采纳率88.2%

答：分式的裂项知识
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+1/(x+4)(x+5)=5/x^2+11x-708
1/x-1/(x+1)+1/(x+1)-1/(x+2)+.+1/(x+4)-1/(x+5)=5/(x^2+11x-708)
1/x-1/(x+5)=5/(x^2+11x-708)
(x+5-x)/(x^2+5x)=5/(x^2+11x-708)
5x^2+55x-3540=5x^2+10x
45x=3540
x=236/3
经检验,x=236/3是原分式方程的根

1年前查看全部

探索计算：1/x(x+1)+1/(x+1)(x+2)+.+1/(x+4(x+5)会做的麻烦回复一下告诉我谢谢急求答案

ppp36631年前1

xuehua1314 共回答了18个问题 | 采纳率88.9%

下方转化为x(x+1)(x+2)(x+3)(x+4)(x+5)
即[(x+2)(x+3)(x+4)(x+5)+x(x+3)(x+4)(x+5)+x(x+1)(x+4)(x+5)+x(x+1)(x+2)(x+5)+x(x+1)(x+2)(x+3)]/x(x+1)(x+2)(x+3)(x+4)(x+5)
后面自己做吧

1年前查看全部

化简1/x(x+1)+1/(x+1)(x+2)+…+1/(x+2010)(x+2011),并求当x=1时该代数式的值.

kokokala1年前3

nylxxlxx 共回答了20个问题 | 采纳率90%

1年前查看全部

计算1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3).+1/(x+2003)(x+2004)

计算1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3).+1/(x+2003)(x+2004)
求全过程 谁能告诉我1/x-1/(x+1)是什么意思?怎么表达,是不是两个分数线?

zhengke441年前1

虞美人m 共回答了18个问题 | 采纳率94.4%

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3).+1/(x+2003)(x+2004)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3).+1/(x+2003)-1/(x+2004)
=1/x-1/(x+2004)
=2004/（x²+2004x)
1/x-1/(x+1) 是分式1/x与1/(x+1)的差.
=(x+1-x)/x(x+1)
=1/x(x+1）

1年前查看全部

分式方程1/(x+1)+1/(x-1）=0的解

有蒲菡萏1年前5

u1u1u1 共回答了19个问题 | 采纳率94.7%

两边乘(x+1)(x-1)
x-1+x+1=0
x=0

1年前查看全部

如何化简下列算式1/x+1/x(x+1)+1/(x+1)(x+2)+...+1/(x+2004)(x+2005) 如何求

如何化简下列算式1/x+1/x(x+1)+1/(x+1)(x+2)+...+1/(x+2004)(x+2005) 如何求解下面的分式方程1/x(x+2)+1/(

dickens065311年前1

llaxh 共回答了21个问题 | 采纳率90.5%

1/x+1/x(x+1)+1/(x+1)(x+2)+...+1/(x+2004)(x+2005)
=1/x + 1/x -1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+2004)-1/(x+2005)
=1/x+1/x-1/(x+2005)
= [2(x+2005)-x]/[ x(x+2005)]
=(x+4010)/[ x(x+2005)]
同理
1/x(x+2) =1/2 [1/X-1/(X+2)]

1年前查看全部

解方程:1/x+1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+9)(x+10)=

解方程:1/x+1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+9)(x+10)=0

lzh75531年前1

77730 共回答了14个问题 | 采纳率92.9%

1/x+1/x-1/(x+1)+1/(x+1)-1/(x+2)+.+1/(x+9)-1/(x+10)=0
2/x-1/(x+10)=0
2(x+10)-x=0
x=-20

1年前查看全部

1/x(x+1)+1/(x+1)(x+2)+…+1/（x+4)(x+5) 求 ①（x-1/y)÷（y-1/x) ②约分

1/x(x+1)+1/(x+1)(x+2)+…+1/（x+4)(x+5) 求 ①（x-1/y)÷（y-1/x) ②约分 4（x的平方＋4x+4)/6(x的平方－4）

园_园1年前1

apc6019 共回答了25个问题 | 采纳率88%

①（x-1/y)÷（y-1/x)
=(xy-1)/y÷(xy-1)/x
=x/y
②约分 4（x的平方＋4x+4)/6(x的平方－4）
x^2+4x+4=(x+2)^2
x^2-4=(x-2)(x+2)
可得 2(x+2)/3(x-2)=(2x+4)/(3x-6)

1年前查看全部

计算1/X(X+1)+1/(X+1)(X+2)+.+1/(X+8)(X+9)

计算1/X(X+1)+1/(X+1)(X+2)+.+1/(X+8)(X+9)
①1/(1-X)+1/(1+X)+2/(1+X^2)+4/(1+X^4)
②1/(1+X)+2/(1+X^2)+4/(1+X^4)+8/(1+X^8)

zhaoshunshun1年前1

左氏三十二 共回答了23个问题 | 采纳率91.3%

1/X(X+1)+1/(X+1)(X+2)+.+1/(X+8)(X+9)
=1/x-1/(x+1)+1/(x+1)-1/(x+1)+...+1/(x+8)-1/(x+9)
=1/x-1(x+9)
=9/x(x+9)
如追加其它问题,采纳本题后点击想我求助,

1年前查看全部

计算：1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+9)(x+10)

2008foreverlove1年前2

无身无色 共回答了11个问题 | 采纳率72.7%

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+9)(x+10)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+……+1/(x+9)-1/(x+10)
=1/x-1/(x+10)
=(x+10-x)/{x(x+10)}
= 10/{x(x+10)}

1年前查看全部

计算1/x(x+1)+1/（x+2）（x+1）.+1/(x+2008)(x+2009)并求当x=1时,该代数式的值

61452f9d0f1c17af1年前6

www4441 共回答了13个问题 | 采纳率100%

1/x(x+1)=1/x-1/(1+x)
1/（x+2)(x+1)=1/(x+1)-1/(x+2)
.
1/(x+2008)(x+2009)=1/(x+2008)-1/(1+2009)
1/x(x+1)+1/（x+2）（x+1）.+1/(x+2008)(x+2009)=1/x-1/(1+x)+1/(x+1)-1/(x+2)+.+1/(x+2008)-1/(x+2009)
=1-1/(x+2009)
1-1/(1+2009)=1-1/2010=2009/2010

1年前查看全部

解13/(x-4)-10/(x-3)=4/(x-5)-1/(x-1) 1/(x+1)+1/(x+7)=1/(x+5)+1

解13/(x-4)-10/(x-3)=4/(x-5)-1/(x-1) 1/(x+1)+1/(x+7)=1/(x+5)+1/(x+3) 的简便方法 要简便的

fengpeijie1年前1

冷月飞觞 共回答了17个问题 | 采纳率82.4%

13/(x-4)-10/(x-3)=4/(x-5)-1/(x-1)
左右两边分别通分得
（3x+1)/(x-4)(x-3)=(3x+1)/(x-5)(x-1)
∴3x+1=0或(x-4)(x-3)=(x-5)(x-1)
∴x=-1/3或x=7
1/(x+1)+1/(x+7)=1/(x+5)+1/(x+3)
2(x+4)/(x²+8x+7)=2(x+4)/(x²+8x+8)
x+4=0或x²+8x+7=x²+8x+8(无义)
x=-4

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lim(1/(x+1)+1/(x^2-1)) x->-1 求极限

liulibo4154761241年前1

xuefeng183 共回答了13个问题 | 采纳率92.3%

原式=lim(x->-1) [(x-1+1)/(x+1)(x-1)]
=lim(x->-1) [x/(x+1)(x-1)]
因为
lim(x->-1) [(x+1)(x-1)/x]=0
所以
原式=∞.

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化简1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3),其中x^2+3x+1=0

安臣1年前1

sumace 共回答了17个问题 | 采纳率82.4%

原式=[1/x-1/(x+1)]+[1/(x+1)-1/(x+2)]+[1/(x+2)-1/(x+3)]
=1/x-1/(x+3)
=2/(x^2+3x)
=2/(-1)
=-2

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初二分式的加减法 1/x(x+1)+1/(x+1)(x+2)+...+1/（x+8）（x+9）

leecz86111年前1

怡人美美 共回答了20个问题 | 采纳率100%

1/x(x+1)
=[(x+1)-x]/x(x+1)
=(x+1)/x(x+1)-x/x(x+1)
=1/x-1/(x+1)
同理
1/(x+1)(x+2)
=[(x+2)-(x+1)]/(x+1)(x+2)
=1/(x+1)-1/(x+2)
以此类推
原式=1/x-1/(x+1)+1/(x+1)-1/(x+2)+……+1/(x+8)-1/(x+9)
中间正负抵消
=1/x-1/(x+9)
=9/x(x+9)

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计算1/X(X+1)+1/(X+1)(X+2)+.+1/(X+99)(X+100)

菜菜加饭饭1年前1

机灵小可 共回答了17个问题 | 采纳率88.2%

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

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（1/(x+1)+1/(x+4))*3+(x-3)*1/(x+4)=1,怎么解,快点谢谢了

spdns1年前2

zmbg 共回答了21个问题 | 采纳率95.2%

通分
3(x+4)+3(x+1)+(x-3)(x+1) = (x+1)(x+4),x≠-1,-4
3x+12+3x+3+x²-2x-3=x²+5x+4
-x+8=0
x=8

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解分式方程:1/x(x+1)+1/(x+1)(x+2)+...+1/(2x-1).2x=1/8

ww破车1年前3

明辨是非的鱼 共回答了13个问题 | 采纳率100%

1/x(x+1)+1/(x+1)(x+2)+...+1/(2x-1).2x
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+…+1/(2x-1)-1/2x
=1/x-1/2x
=1/2x=1/8
解得：x=4.

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1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+99)(x+100)=_____

jefferyyuan1年前1

清筱荷 共回答了16个问题 | 采纳率81.3%

1/x(x+1)=1/x-1/(x+1)
1/(x+1)(x+2)=1/(x+1)-1/(x+2)
1/(x+2)(x+3)=1/(x+2)-1/(x+3)
.
1/(x+99)(x+100)=1/(X+99)-1/(X+100)
很明显,这些数相加的话,中间部分正好是加减抵消.
最后
原式=1/x-1/(X+100)
=(x+100-x)/x(x+100)
=100/x(x+100)

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解方程1/x+1/(x+1)+1/(x+2)+1/(x+3)=19/20.

八度创维1年前4

bilive 共回答了20个问题 | 采纳率85%

X=3；
应该没有简单的方法,只能通分求解了,
这个题应该是考你计算耐心的吧.
希望我的回答对你有所帮助.

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F(x)=lnx/(x+1)+1/x 若x>0且X不等于1时 F(x)> lnx/(x+1)+k/x恒成立 求K的取值

思与行1年前2

hungbinerS 共回答了21个问题 | 采纳率90.5%

由题意得：lnx/(x+1)+1/x > lnx/(x+1)+k/x
所以1/x＞k/x
因为X大于0,两边同乘x得1＞k即k＜1
这里不用讨论的,因为x是正的,不等式两边同乘上一个正数符号不变.（同乘上一个负数符号要变的）

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数学导数系数取值问题求解已知函数f(x)=(lnx)/(x+1)+1/x,如果x大于0 x ≠1时,f(x)大于lnx/

数学导数系数取值问题求解
已知函数f(x)=(lnx)/(x+1)+1/x,如果x大于0 x ≠1时,f(x)大于lnx/(x-1)+k/x,求k的取值范围. 要过程,分不是问题,谢了.

时间海ar1年前1

y2kkao 共回答了14个问题 | 采纳率100%

令y=(lnx)/(x+1) + 1/x - lnx/(x-1) - k/x→当x＞0,且x≠1时,xlnx/(x-1)＜(1-k)/2.令z=xlnx/(x-1)→z'=[x - 1 - (x+1)lnx]/(x-1) 令w=x - 1 - (x+1)lnx→w'=x - 1/x - 2xlnx→w''=1/x - 2lnx - 1→w'''= -2(x+1)/x 易知：当x＞0时,w'''＜0→w''单调递减.当x=1时,w''=0→当0＜x＜1时,w''＞0→w'单调递增；当x＞1时,w''＜0→w'单调递减.当x=1时,w'=0→当x＞0,且x≠1时,w'＜0→w单调递减.当x=1时,w=0→当0＜x＜1时,w＞0→z单调递增；当x＞1时,w＜0→z单调递减.易得：lim(x→1) xlnx/(x-1)=1/2→当x＞0,且x≠1时,xlnx/(x-1)＜1/2 由xlnx/(x-1)＜(1-k)/2,xlnx/(x-1)＜1/2→k≤0 故：k的取值范围是k≤0

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