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6 tháng 2 2022

a)\(-1,6:\left(1+\dfrac{2}{3}\right)=-1,6:\dfrac{5}{3}=-\dfrac{8}{5}.\dfrac{3}{5}=\dfrac{-24}{25}\)

b)\(\left(\dfrac{-2}{3}\right)+\dfrac{3}{4}-\left(-\dfrac{1}{6}\right)+\left(\dfrac{-2}{5}\right)=-\dfrac{2}{3}+\dfrac{3}{4}+\dfrac{1}{6}-\dfrac{2}{5}=\dfrac{-40+45+10-24}{60}=\dfrac{-9}{60}=\dfrac{-3}{20}\)

c)\(\left(\dfrac{-3}{7}:\dfrac{2}{11}+\dfrac{-4}{7}:\dfrac{2}{11}\right).\dfrac{7}{33}=\left(\dfrac{-3}{7}.\dfrac{11}{2}+\dfrac{-4}{7}.\dfrac{11}{2}\right).\dfrac{7}{33}=\left[\dfrac{11}{2}\left(\dfrac{-3}{7}+\dfrac{-4}{7}\right)\right].\dfrac{7}{33}=\dfrac{-11}{2}.\dfrac{7}{33}=\dfrac{-7}{6}\)

d)\(\dfrac{-5}{8}+\dfrac{4}{9}:\left(\dfrac{-2}{3}\right)-\dfrac{7}{20}.\left(\dfrac{-5}{14}\right)=\dfrac{-5}{8}-\dfrac{4}{9}.\dfrac{3}{2}+\dfrac{1}{8}=\dfrac{-5}{8}+\dfrac{1}{8}-\dfrac{2}{3}=-\dfrac{7}{6}\)

18 tháng 3 2022

\(\dfrac{3}{1.4}+\dfrac{3}{4.7}+...+\dfrac{3}{100.103}\\ =1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{100}-\dfrac{1}{103}\\ =1-\dfrac{1}{103}\\ =\dfrac{102}{103}\)

24 tháng 2 2022

\(\dfrac{x-7}{7}=\dfrac{y-6}{6}=\dfrac{x-y-1}{1}=\dfrac{-4-1}{1}=-5\)

\(\Rightarrow x-7=7.\left(-5\right)=-35\Rightarrow x=-28;y-6=6.\left(-5\right)=-30\Rightarrow y=-24\)

24 tháng 2 2022

\(\Leftrightarrow6\left(x-7\right)=7\left(y-6\right)\)

\(\Leftrightarrow6x-42=7y-42\)

\(\Leftrightarrow6x=7y\)

\(\Leftrightarrow6\left(x-y\right)-y=0\)

\(\Leftrightarrow-24-y=0\)

\(\Leftrightarrow y=-24\)

\(\Leftrightarrow\dfrac{x-7}{-24-6}=\dfrac{7}{6}\Leftrightarrow\dfrac{x-7}{-30}=\dfrac{7}{6}\Leftrightarrow6x-30=-210\Leftrightarrow6x=-180\Leftrightarrow x=-30\)

23 tháng 2 2022

\(\dfrac{4}{1.5}+\dfrac{4}{5.9}+\dfrac{4}{9.13}+...+\dfrac{4}{97.101}\\ =1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{13}+...+\dfrac{1}{97}-\dfrac{1}{101}\\ =1-\dfrac{1}{101}\\ =\dfrac{100}{101}\)

23 tháng 2 2022

ko

25 tháng 2 2022

Để A là phân số thì

\(n^2-25\ne0\\ \Leftrightarrow n^2\ne25\\ \Leftrightarrow n\ne\pm5\)

23 tháng 2 2022

\(\dfrac{x-2}{3}=\dfrac{x+5}{4}\\ \Rightarrow4\left(x-2\right)=3\left(x+5\right)\\ \Rightarrow4x-8=3x+15\\ \Rightarrow x-23=0\\ \Rightarrow x=23\)

24 tháng 2 2022

\(\Leftrightarrow\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+....+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{2009}{2010}\)

\(\Leftrightarrow1-\dfrac{1}{x+1}=\dfrac{2009}{2010}\)

\(\Leftrightarrow-\dfrac{1}{x+1}=-\dfrac{1}{2010}\)

\(\Leftrightarrow x+1=2010\Leftrightarrow x=2009\)

 

 

 

 

 

 

7 tháng 3 2022

= 23,18 - 3,18 - 4,17 - 5,83 + 51,54 + 8,46

= 20 - 10 + 60

= 70

= 23,18 - 3,18 - 4,17 - 5,83 + 51,54 + 8,46

= 20 - 10 + 60

= 70