\(A=\frac{2010}{2011}\)

h giup minh voi

\(tuA=1003+1007+\dfrac{2010}{113}+\dfrac{2010}{117}-\dfrac{2010}{119}=2010\left(1+\dfrac{1}{113}+\dfrac{1}{117}-\dfrac{1}{119}\right)\)\(mauA=1003+1008+\dfrac{2011}{113}+\dfrac{2011}{117}-\dfrac{2011}{119}=2011\left(1+\dfrac{1}{113}+\dfrac{1}{117}-\dfrac{1}{119}\right)\)có \(\left(1+\dfrac{1}{113}+\dfrac{1}{117}-\dfrac{1}{119}\right)\ne0=>A=\dfrac{2010}{2011}\)

Đề ???

\(A=\frac{1003+1007+\frac{2010}{113}+\frac{2010}{117}-\frac{1003}{119}-\frac{1007}{119}}{1003+1008+\frac{2011}{113}+\frac{2011}{117}-\frac{1003}{119}-\frac{1008}{119}}\)

\(=\frac{2010+\frac{2010}{113}+\frac{2010}{117}-\frac{2010}{119}}{2011+\frac{2011}{113}+\frac{2011}{117}-\frac{2011}{119}}\)

\(=\frac{2010.\left(1+\frac{1}{113}+\frac{1}{117}-\frac{1}{119}\right)}{2011.\left(1+\frac{1}{113}+\frac{1}{117}-\frac{1}{119}\right)}\)

\(=\frac{2010}{2011}\)

\(A=\frac{1003+1007+\frac{2010}{113}+\frac{2010}{117}-\frac{100}{119}-\frac{1007}{119}}{1003+1008+\frac{2011}{113}+\frac{2011}{117}-\frac{1003}{119}-\frac{1008}{119}}\)

\(A=\frac{1003+1008+\frac{2011}{113}+\frac{2011}{117}-\frac{1003}{119}-\frac{1008}{119}}{1003+1008+\frac{2011}{113}+\frac{2011}{117}-\frac{1003}{119}-\frac{1008}{119}}\)+       \(\frac{1+\frac{1}{113}+\frac{1}{117}-\frac{903}{119}-\frac{1}{119}}{1003+1008+\frac{2011}{113}+\frac{2011}{117}-\frac{1003}{119}-\frac{1008}{119}}\)          

\(A=1+\frac{1+\frac{1}{113}+\frac{1}{117}-\frac{904}{119}}{2011+\frac{2011}{113}+\frac{2011}{117}-\frac{2011}{119}}\) 

\(A=\frac{1+\frac{1}{113}+\frac{1}{117}-\frac{1}{119}-\frac{90.}{119}}{2011+2011.\left(\frac{1}{113}+\frac{1}{117}-\frac{1}{119}\right)}\)

\(A=\frac{\frac{90}{119}}{2010+2011}\)

\(A=\frac{\frac{90}{119}}{4021}\)

cho mình hỏi làm thế nào để k cho người khác vậy?????

Ta có:

\(A=\dfrac{1003+1007+\dfrac{2010}{113}+\dfrac{2010}{117}-\dfrac{1003}{119}-\dfrac{1007}{119}}{1003+1008+\dfrac{2011}{113}+\dfrac{2011}{117}-\dfrac{1003}{119}-\dfrac{1007}{119}}\)

\(A=\dfrac{2010+\dfrac{2010}{113}+\dfrac{2010}{117}-\dfrac{2010}{119}}{2011+\dfrac{2011}{113}+\dfrac{2011}{117}-\dfrac{2011}{119}}\)

\(A=\dfrac{2010.\left(\dfrac{1}{1}+\dfrac{1}{113}+\dfrac{1}{117}-\dfrac{1}{119}\right)}{2013.\left(\dfrac{1}{1}+\dfrac{1}{113}+\dfrac{1}{117}+\dfrac{1}{119}\right)}\)

\(\Rightarrow A=\dfrac{2010}{2013}\)

= \(\dfrac{2028,076341}{2029,093738}\) hoặc 0,9994985954.