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Đề ???
\(A=\frac{1003+1007+\frac{2010}{113}+\frac{2010}{117}-\frac{1003}{119}-\frac{1007}{119}}{1003+1008+\frac{2011}{113}+\frac{2011}{117}-\frac{1003}{119}-\frac{1008}{119}}\)
\(=\frac{2010+\frac{2010}{113}+\frac{2010}{117}-\frac{2010}{119}}{2011+\frac{2011}{113}+\frac{2011}{117}-\frac{2011}{119}}\)
\(=\frac{2010.\left(1+\frac{1}{113}+\frac{1}{117}-\frac{1}{119}\right)}{2011.\left(1+\frac{1}{113}+\frac{1}{117}-\frac{1}{119}\right)}\)
\(=\frac{2010}{2011}\)
\(A=\frac{1003+1007+\frac{2010}{113}+\frac{2010}{117}-\frac{100}{119}-\frac{1007}{119}}{1003+1008+\frac{2011}{113}+\frac{2011}{117}-\frac{1003}{119}-\frac{1008}{119}}\)
\(A=\frac{1003+1008+\frac{2011}{113}+\frac{2011}{117}-\frac{1003}{119}-\frac{1008}{119}}{1003+1008+\frac{2011}{113}+\frac{2011}{117}-\frac{1003}{119}-\frac{1008}{119}}\)+ \(\frac{1+\frac{1}{113}+\frac{1}{117}-\frac{903}{119}-\frac{1}{119}}{1003+1008+\frac{2011}{113}+\frac{2011}{117}-\frac{1003}{119}-\frac{1008}{119}}\)
\(A=1+\frac{1+\frac{1}{113}+\frac{1}{117}-\frac{904}{119}}{2011+\frac{2011}{113}+\frac{2011}{117}-\frac{2011}{119}}\)
\(A=\frac{1+\frac{1}{113}+\frac{1}{117}-\frac{1}{119}-\frac{90.}{119}}{2011+2011.\left(\frac{1}{113}+\frac{1}{117}-\frac{1}{119}\right)}\)
\(A=\frac{\frac{90}{119}}{2010+2011}\)
\(A=\frac{\frac{90}{119}}{4021}\)
\(tuA=1003+1007+\dfrac{2010}{113}+\dfrac{2010}{117}-\dfrac{2010}{119}=2010\left(1+\dfrac{1}{113}+\dfrac{1}{117}-\dfrac{1}{119}\right)\)\(mauA=1003+1008+\dfrac{2011}{113}+\dfrac{2011}{117}-\dfrac{2011}{119}=2011\left(1+\dfrac{1}{113}+\dfrac{1}{117}-\dfrac{1}{119}\right)\)có \(\left(1+\dfrac{1}{113}+\dfrac{1}{117}-\dfrac{1}{119}\right)\ne0=>A=\dfrac{2010}{2011}\)
\(B=\frac{1010+1007+\frac{2017}{113}+\frac{2017}{117}-\frac{1010}{119}-\frac{1007}{119}}{1010+1008+\frac{2018}{113}+\frac{2018}{117}-\frac{1010}{119}-\frac{1008}{119}}\)
\(B=\frac{2017+\frac{2017}{113}+\frac{2017}{117}-\frac{2017}{119}}{2018+\frac{2018}{113}+\frac{2018}{117}-\frac{2018}{119}}\)
\(B=\frac{2017.\left(1+\frac{1}{113}+\frac{1}{117}-\frac{1}{119}\right)}{2018.\left(1+\frac{1}{113}+\frac{1}{117}-\frac{1}{119}\right)}\)
\(B=\frac{2017}{2018}\)
Vậy \(B=\frac{2017}{2018}\)
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