câu 1 

=> x+1/2+x+1/3+x+1/4-x-1/5-x-1/6=0

=> (x+x+x-x-x)+(1/2+1/3+1/4-1/5-1/6)=0

=> x+43/60=0

=> x = -43/60

câu dưới làm tương tự bạn nhé!

a, 

\(=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{x.\left(x+2\right)}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+2}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{x+2}\right)\)

\(=\frac{1}{2}\times\frac{x+1}{x+2}\)

\(=\frac{2x+2}{x+2}\)

Hơ hơ =v

Làm đại phần a đúng sai mặc kệ ~~

a,

\(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{x\left(x+2\right)}\)

\(=\frac{1}{2}\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{x\left(x+2\right)}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{x+2}\right)\)

\(=\frac{1}{2}\cdot\frac{x+1}{x+2}\)

\(=\frac{2x+2}{x+2}\)

b,

x = 1.2 + 2.3 + 3.4 + ....+ 89.90

3x = 1.2.3 + 2.3.3 + 3.4.3 + .... + 89.90

3x = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 89.90.(91 - 88)

3x = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 89.90.91 - 88.89.90

3x = 89.90.91

x = \(\frac{89\cdot90\cdot91}{3}=242970\)

a) Đặt \(A=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{x.\left(x+2\right)}\)

\(\Rightarrow2A=(1-\frac{1}{3})+(\frac{1}{3}-\frac{1}{5})+...+(\frac{1}{x}-\frac{1}{x+2})\)

\(\Rightarrow A=1-\frac{1}{x+2}=\frac{x+1}{x+2}\)

b)\(x=1.2+2.3+3.4+...+89.90\)

\(\Rightarrow3x=1.2.(3-0)+2.3.(4-1)+...+89.98.(100-88)\)

\(\Rightarrow3x=1.2.3+2.3.4-1.2.3+...+89.90.100-88.89.90\)

\(\Rightarrow3x=89.90.100=872200\)

\(\Rightarrow x=\frac{872200}{3}\)

x=-100

6: =>x=9/10+1/5=9/10+2/10=11/10

7: =>x=3/8-5/12=36/96-40/96=-1/24

8: =>x=7/6-5/4=14/12-15/12=-1/12

9: =>x=1/35+2/7=1/35+10/35=11/35

10: =>x=2/7-7/10=20/70-49/70=-29/70

1, \(x=-\dfrac{5}{3}-\dfrac{1}{2}=-\dfrac{10}{6}-\dfrac{3}{6}=-\dfrac{13}{6}\)

2, \(x=\dfrac{1}{3}-\dfrac{3}{5}=\dfrac{5-9}{15}=-\dfrac{4}{15}\)

4, \(x=-\dfrac{7}{9}+\dfrac{4}{3}=\dfrac{-7+12}{9}=\dfrac{5}{9}\)

5, \(x=\dfrac{5}{6}-\dfrac{7}{3}=\dfrac{5-14}{6}=-\dfrac{9}{6}=-\dfrac{3}{2}\)

6, \(x=\dfrac{9}{10}+\dfrac{1}{5}=\dfrac{9+2}{10}=\dfrac{11}{10}\)

7, \(x=\dfrac{3}{8}-\dfrac{5}{12}=\dfrac{9-10}{12}=-\dfrac{1}{12}\)

8, \(x=\dfrac{7}{6}-\dfrac{5}{4}=\dfrac{14-15}{12}=-\dfrac{1}{12}\)

9, \(x=\dfrac{1}{35}+\dfrac{2}{7}=\dfrac{1+10}{35}=\dfrac{11}{35}\)

10, \(x=-\dfrac{7}{10}+\dfrac{2}{7}=\dfrac{-49+20}{70}=\dfrac{-29}{70}\)

a) \(\frac{x+1}{94}+\frac{x+2}{93}+\frac{x+3}{92}=\frac{x+4}{91}+\frac{x+5}{90}+\frac{x+6}{89}\)

\(\Leftrightarrow\left(\frac{x+1}{94}+1\right)+\left(\frac{x+2}{93}+1\right)+\left(\frac{x+3}{92}+1\right)=\left(\frac{x+4}{91}+1\right)+\left(\frac{x+5}{90}+1\right)+\left(\frac{x+6}{89}+1\right)\)

\(\Leftrightarrow\frac{x+95}{94}+\frac{x+95}{93}+\frac{x+95}{92}-\frac{x+95}{91}-\frac{x+95}{90}-\frac{x+95}{89}=0\)

\(\Leftrightarrow\) \(\left(x+95\right)\left(\frac{1}{94}+\frac{1}{93}+\frac{1}{92}-\frac{1}{91}-\frac{1}{90}-\frac{1}{89}\right)=0\)

Vì \(\frac{1}{94}+\frac{1}{93}+\frac{1}{92}-\frac{1}{91}-\frac{1}{90}-\frac{1}{89}\ne0\)

\(\Rightarrow x+95=0\)

\(\Leftrightarrow x=-95\)

Vậy phương trình có một nghiệm x = -95

b) \(\frac{x-1}{59}+\frac{x-2}{58}+\frac{x-3}{57}=\frac{x-4}{56}+\frac{x-5}{55}+\frac{x-6}{54}\)

\(\Leftrightarrow\left(\frac{x-1}{59}-1\right)+\left(\frac{x-2}{58}-1\right)+\left(\frac{x-3}{57}-1\right)=\left(\frac{x-4}{56}-1\right)+\left(\frac{x-5}{55}-1\right)+\left(\frac{x-6}{54}-1\right)\)

\(\Leftrightarrow\frac{x-60}{59}+\frac{x-60}{58}+\frac{x-60}{57}-\frac{x-60}{56}-\frac{x-60}{55}-\frac{x-60}{54}=0\)

\(\Leftrightarrow\left(x-60\right)\left(\frac{1}{59}+\frac{1}{58}+\frac{1}{57}-\frac{1}{56}-\frac{1}{55}-\frac{1}{54}\right)=0\)

Vì \(\frac{1}{59}+\frac{1}{58}+\frac{1}{57}-\frac{1}{56}-\frac{1}{55}-\frac{1}{54}\ne0\)

\(\Rightarrow x-60=0\)

\(\Leftrightarrow x=60\)

Vậy phương trình có một nghiệm x = 60

a) \(\frac{x+1}{94}+\frac{x+2}{93}+\frac{x+3}{92}=\frac{x+4}{91}+\frac{x+5}{90}+\frac{x+6}{89}\)

\(\Rightarrow\left(\frac{x+1}{94}+1\right)+\left(\frac{x+2}{93}+1\right)+\left(\frac{x+3}{92}+1\right)=\left(\frac{x+4}{91}+1\right)+\left(\frac{x+5}{90}+1\right)+\left(\frac{x+6}{89}+1\right)\)

\(\Rightarrow\frac{x+95}{94}+\frac{x+95}{93}+\frac{x+95}{92}=\frac{x+95}{91}+\frac{x+95}{90}+\frac{x+95}{89}\)

\(\Rightarrow\frac{x+95}{94}+\frac{x+95}{93}+\frac{x+95}{92}-\frac{x+95}{91}-\frac{x+95}{90}-\frac{x+95}{89}=0\)

\(\Rightarrow\left(x+95\right)\left(\frac{1}{94}+\frac{1}{93}+\frac{1}{92}-\frac{1}{91}-\frac{1}{90}-\frac{1}{89}\right)=0\)

Mà \(\frac{1}{94}+\frac{1}{93}+\frac{1}{92}-\frac{1}{91}-\frac{1}{90}-\frac{1}{89}\ne0\)

\(\Rightarrow x+95=0\)

\(\Rightarrow x=-95\)

Vậy x = -95

b) \(\frac{x-1}{59}+\frac{x-2}{58}+\frac{x-3}{57}=\frac{x-4}{56}+\frac{x-5}{55}+\frac{x-6}{54}\)

\(\Rightarrow\left(\frac{x-1}{59}-1\right)+\left(\frac{x-2}{58}-1\right)+\left(\frac{x-3}{57}-1\right)=\left(\frac{x-4}{56}-1\right)+\left(\frac{x-5}{55}-1\right)+\left(\frac{x-6}{54}-1\right)\)

\(\Rightarrow\frac{x-60}{59}+\frac{x-60}{58}+\frac{x-60}{57}-\frac{x-60}{56}-\frac{x-5}{55}-\frac{x-6}{54}=0\)

\(\Rightarrow\left(x-60\right)\left(\frac{1}{59}+\frac{1}{58}+\frac{1}{57}-\frac{1}{56}-\frac{1}{55}-\frac{1}{54}\right)=0\)

Mà \(\frac{1}{59}+\frac{1}{58}+\frac{1}{57}-\frac{1}{56}-\frac{1}{55}-\frac{1}{54}\ne0\)

\(\Rightarrow x-60=0\)

\(\Rightarrow x=60\)

Vậy x = 60

\(\frac{x+1}{94}+\frac{x+2}{93}+\frac{x+3}{92}=\frac{x+4}{91}+\frac{x+5}{90}+\frac{x+6}{89}\)

\(\Leftrightarrow\frac{x+1}{94}+1+\frac{x+2}{93}+1+\frac{x+3}{92}+1=\frac{x+4}{91}+1+\frac{x+5}{90}+1+\frac{x+6}{89}+1\)

\(\Leftrightarrow\frac{x+95}{94}+\frac{x+95}{93}+\frac{x+95}{92}=\frac{x+95}{91}+\frac{x+95}{90}+\frac{x+95}{89}\)

\(\Leftrightarrow\frac{x+95}{94}+\frac{x+95}{93}+\frac{x+95}{92}-\frac{x+95}{91}-\frac{x+95}{90}-\frac{x+95}{89}=0\)

\(\Leftrightarrow\left(x+95\right)\left(\frac{1}{94}+\frac{1}{93}+\frac{1}{92}-\frac{1}{91}-\frac{1}{90}-\frac{1}{89}\right)=0\)

\(\Leftrightarrow x+95=0\).Do \(\frac{1}{94}+\frac{1}{93}+\frac{1}{92}-\frac{1}{91}-\frac{1}{90}-\frac{1}{89}\ne0\)

\(\Leftrightarrow x=-95\)

(x+1)/94 + ( x+2)/93 + ( x+3)/92.......

= ................ + ( x+6)/89 
<=> (x+1)/94 + 1 + ( x+2)/93 +1 .........

=.............. cộng 1 nhá 
<=> (x+95)/94 + ( x+96) / 93 + ( x+95)/92

= ( x+95)/91 + ( x+95)/90 + ( x+95)/89 
<=> ( x+95) ( 1/94 +1/93 +1/92 )

= ( x+95) ( 1/91 +1/90 +1/89) 
<=> ( x+95) ( 1/94 +1/93 +1/92 - 1/91 - 1/90 - 1/89 ) 
<=> x+95 =0 
<=>x = -95 
Vậy :x = -95

Zui lòng chia nhỏ

1: =>x=-5/3-1/2=-13/6

2: =>x=1/3-3/5=-4/15

4: =>x=-7/9+4/3=-7/9+12/9=5/9

5: =>x=5/6-7/3=5/6-14/6=-9/6=-3/2

6: =>x=9/10+1/5=11/10

7: =>x=3/8-5/12=36/96-40/96=-1/24

8: Đề sai rồi bạn