Trong các phân số sau : \(\dfrac{1007}{1008}\), \(\dfrac{1008}{1007}\), \(\dfrac{10081007}{10071008}\) phân số nào nhân với \(\dfrac{7}{8}\)sẽ cho kết quả bé hơn \(\dfrac{7}{8}\).
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20 tháng 7 2017
\(\dfrac{x+1}{2014}+\dfrac{x+2}{2013}+.....+\dfrac{x+1007}{1008}=\dfrac{x+1008}{1007}+\dfrac{x+1009}{1006}+........+\dfrac{x+2014}{1}\)\(\Leftrightarrow\left(\dfrac{x+1}{2014}+1\right)+\left(\dfrac{x+2}{2013}+1\right)+...+\left(\dfrac{x+1007}{1008}+1\right)=\left(\dfrac{x+1008}{1007}+1\right)+\left(\dfrac{x+1009}{1006}+1\right)+...+\left(\dfrac{x+2014}{1}+1\right)\)\(\Leftrightarrow\dfrac{x+2015}{2014}+\dfrac{x+2015}{2013}+...+\dfrac{x+1007}{1008}=\dfrac{x+2015}{1007}+\dfrac{x+1009}{1006}+...+\dfrac{x+2014}{1}\)\(\Leftrightarrow\dfrac{x+2015}{2014}+\dfrac{x+2015}{2013}+...+\dfrac{x+2015}{1008}-\dfrac{x+1008}{1007}-\dfrac{x+2015}{1006}-...-\dfrac{x+2015}{1}=0\)\(\Leftrightarrow\left(x+2015\right)\left(\dfrac{1}{2014}+\dfrac{1}{2013}+...+\dfrac{1}{1008}-\dfrac{1}{1007}-\dfrac{1}{1006}-...-1\right)=0\)\(\Leftrightarrow x+2015=0\left(\dfrac{1}{2014}+\dfrac{1}{2013}+...+\dfrac{1}{1008}-\dfrac{1}{1007}-\dfrac{1}{1006}-...-1>0\right)\)\(\Leftrightarrow x=-2015\)
Vậy x=-2015
22 tháng 3 2018
\(tuA=1003+1007+\dfrac{2010}{113}+\dfrac{2010}{117}-\dfrac{2010}{119}=2010\left(1+\dfrac{1}{113}+\dfrac{1}{117}-\dfrac{1}{119}\right)\)\(mauA=1003+1008+\dfrac{2011}{113}+\dfrac{2011}{117}-\dfrac{2011}{119}=2011\left(1+\dfrac{1}{113}+\dfrac{1}{117}-\dfrac{1}{119}\right)\)có \(\left(1+\dfrac{1}{113}+\dfrac{1}{117}-\dfrac{1}{119}\right)\ne0=>A=\dfrac{2010}{2011}\)
PT
23 tháng 7 2017
Ta có:
\(A=\dfrac{1003+1007+\dfrac{2010}{113}+\dfrac{2010}{117}-\dfrac{1003}{119}-\dfrac{1007}{119}}{1003+1008+\dfrac{2011}{113}+\dfrac{2011}{117}-\dfrac{1003}{119}-\dfrac{1007}{119}}\)
\(A=\dfrac{2010+\dfrac{2010}{113}+\dfrac{2010}{117}-\dfrac{2010}{119}}{2011+\dfrac{2011}{113}+\dfrac{2011}{117}-\dfrac{2011}{119}}\)
\(A=\dfrac{2010.\left(\dfrac{1}{1}+\dfrac{1}{113}+\dfrac{1}{117}-\dfrac{1}{119}\right)}{2013.\left(\dfrac{1}{1}+\dfrac{1}{113}+\dfrac{1}{117}+\dfrac{1}{119}\right)}\)
\(\Rightarrow A=\dfrac{2010}{2013}\)
8 tháng 4 2023
a: =>\(\dfrac{2x-4}{2014}+\dfrac{2x-2}{2016}< \dfrac{2x-1}{2017}+\dfrac{2x-3}{2015}\)
=>\(\dfrac{2x-2018}{2014}+\dfrac{2x-2018}{2016}< \dfrac{2x-2018}{2017}+\dfrac{2x-2018}{2015}\)
=>2x-2018<0
=>x<2019
b: \(\Leftrightarrow\left(\dfrac{3-x}{100}+\dfrac{4-x}{101}\right)>\dfrac{5-x}{102}+\dfrac{6-x}{103}\)
=>\(\dfrac{x-3}{100}+\dfrac{x-4}{101}-\dfrac{x-5}{102}-\dfrac{x-6}{103}< 0\)
=>\(x+97< 0\)
=>x<-97
\(\dfrac{10081007}{10071008}\)
Thank you bạn Bánh Đậu Xanh, nhưng bạn có thể trình bày rõ hơn được không.