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18 tháng 7 2021

\(-\frac{12}{35}\div\frac{7}{11}-\frac{23}{35}\div\frac{7}{11}-\frac{5}{11}\)

\(=\left(-\frac{12}{35}-\frac{23}{35}\right)\div\frac{7}{11}-\frac{5}{11}\)

\(=-1\div\frac{7}{11}-\frac{5}{11}\)

\(=-\frac{11}{7}-\frac{5}{11}\)

\(=-\frac{156}{77}\)

18 tháng 7 2021

\(2-\frac{11}{9}\div\frac{5}{14}-\frac{7}{9}\times\frac{14}{5}\)

\(=2-\frac{154}{45}-\frac{98}{45}\)

\(=-\frac{64}{45}-\frac{98}{45}\)

\(=-\frac{18}{5}\)

AH
Akai Haruma
Giáo viên
6 tháng 12 2023

Bài 1:

$M=3.4.5+4.5.6+...+13.14.15$

$4M=3.4.5(6-2)+4.5.6(7-3)+....+13.14.15(16-12)$

$=-2.3.4.5+3.4.5.6-3.4.5.6+4.5.6.7+....-12.13.14.15+13.14.15.16$

$=-2.3.4.5+13.14.15.16=43560$

$M=43560:4=10890$

AH
Akai Haruma
Giáo viên
6 tháng 12 2023

Bài 2:

a.

$3M=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{97.100}$

$=\frac{4-1}{1.4}+\frac{7-4}{4.7}+\frac{10-7}{7.10}+...+\frac{100-97}{97.100}$

$=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{97}-\frac{1}{100}$

$=1-\frac{1}{100}=\frac{99}{100}$

$M=\frac{99}{100}:3=\frac{33}{100}$

21 tháng 8 2015

\(a,\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{43.45}=\frac{5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{43.45}\right)=\frac{5}{3}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{43}-\frac{1}{45}\right)=\frac{5}{3}.\frac{44}{45}=\frac{44}{27}\)

19 tháng 6 2020

Rút gọn bằng kiểu nào?

\(P=\frac{5}{3\cdot7}+\frac{5}{7\cdot11}+\frac{5}{11\cdot15}+...+\frac{5}{\left(4n-1\right)\left(4n+3\right)}\)

\(P=\frac{5}{4}\left(\frac{4}{3\cdot7}+\frac{4}{7\cdot11}+\frac{4}{11\cdot15}+...+\frac{4}{\left(4n-1\right)\left(4n+3\right)}\right)\)

\(P=\frac{5}{4}\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{4n+3}\right)\)

\(P=\frac{5}{4}\left(\frac{1}{3}-\frac{1}{4n+3}\right)\)

...

19 tháng 6 2020

P=\(\frac{5}{3x7}\) +\(\frac{5}{7x11}\)+\(\frac{5}{11x15}\)+...+\(\frac{5}{\left(4n-1\right)x\left(4n+3\right)}\)

\(\frac{4}{5}\)P=\(\frac{4}{3x7}\)+\(\frac{4}{7x11}\)+\(\frac{4}{11x15}\)+...+\(\frac{4}{\left(4n-1\right)x\left(4n+3\right)}\)

\(\frac{4}{5}\)P=\(\frac{1}{3}\)-\(\frac{1}{7}\)+\(\frac{1}{7}\)-\(\frac{1}{11}\)+...+\(\frac{1}{4n-1}\)-\(\frac{1}{4n+3}\)

\(\frac{4}{5}\)P=\(\frac{1}{3}\)-\(\frac{1}{4n+3}\)

P=\(\frac{5}{12}\)-\(\frac{5}{16n+12}\)

29 tháng 12 2015

1. -x+20 = -(-15)-8+13

=> -x=15-8+13-20

=> -x=0

=> x=0

2. -(-10)+x=-13+(-9)+(-6)

=> 10+x=-13-9-6

=> x = -13-9-6-10

=> x = -38

3. 8-(-12)+10=-(-14)-x

=> 8+12+10=14-x

=> x = 14-8-12-10

=> x = -16

4. -(+12)+(-x)-(-3)=5-(-7)

=> -12-x+3=5+7

=> -x=5+7+12-3

=> -x=21

=> x=-21

5. 14-x+(-10)=-(-9)+(+15)

=> 14-x-10=9+15

=> -x=9+15-14+10

=> -x=20

=> x=-20

6. 12-(-17)+(-3)=-5+x

=> 12+17-3+5=x

=> x=31

7. x-(-19)-(+32)=14-(+16)

=> x+19-32=14-16

=> x=14-16+32-19

=> x=11

8. x-|-15|-|7|=-(-9)+|-5|

=> x-15-7=9+5

=> x=9+5+7+15

=> x=36

9. 15-x+17=13-(-21)

=> 15-x+17=13+21

=> -x=13+21-15-17

=> -x=2

=> x=-2

10. -|-5|-(-x)+4=3-(-25)

=> -5+x+4=3+25

=> x=3+25-4+5

=> x=29

25 tháng 3 2023

a. \(\dfrac{x}{5}=\dfrac{8}{10}\)

\(\Rightarrow10x=8.5\)

\(\Rightarrow10x=40\)

\(\Rightarrow x=\dfrac{40}{10}=4\)

b. \(\dfrac{9}{x}=\dfrac{90}{100}\)

\(\Rightarrow9.100=90x\)

\(\Rightarrow900=90x\)

\(\Rightarrow x=\dfrac{900}{90}=10\)

c. \(17+\dfrac{x}{35}=\dfrac{5}{7}\)

\(\Rightarrow\dfrac{595+x}{35}=\dfrac{25}{35}\)

\(\Rightarrow595+x=25\)

\(\Rightarrow x=25-595=-570\)

d. \(x:\dfrac{5}{27}=\dfrac{2}{9}\)

\(\Rightarrow\dfrac{27x:5}{27}=\dfrac{6}{27}\)

\(\Rightarrow27x:5=6\)

\(\Rightarrow27x=5.6\)

\(\Rightarrow27x=30\)

\(\Rightarrow x=\dfrac{30}{27}=\dfrac{10}{9}\approx1,11\)

8 tháng 10 2021

a) \(\dfrac{x-3}{x+5}=\dfrac{5}{7}\)

\(7\left(x-3\right)=5\left(x+5\right)\)

\(7x-21=5x+25\)

\(7x-21-5x-25=0\)

\(2x-46=0\)

\(2x=46\)

\(x=23\)

8 tháng 10 2021

giúp mik phần b nha đc ko ???