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\(A=2008.\left(\frac{1}{2007}-\frac{1000}{1004}\right)-2009.\left(\frac{1}{2007}-2\right)\)
\(\Rightarrow A=2008.\frac{1}{2007}-2000-2009.\frac{1}{2007}+4018\)
\(\Rightarrow A=\frac{1}{2007}.\left(2008-2009\right)-2000+4018\)
\(\Rightarrow A=\frac{1}{2007}.\left(-1\right)-2000+4018\)
\(\Rightarrow A\approx2018\)
\(=\dfrac{2008}{2007}-2\cdot2009-\dfrac{2009}{2007}+2009\cdot2\)
=-1/2007
\(=\frac{1004}{2007}\left(\frac{-5}{4}+\frac{-1}{4}-\frac{1}{2}\right)=\frac{1004}{2007}.\left(-2\right)=-\frac{2008}{2007}\)
a: \(=\dfrac{2008}{2007}-2009\cdot2-\dfrac{2009}{2007}+2009\cdot2\)
=-1/2007
b: \(=\dfrac{5^5\cdot5^3\cdot2^6-5^4\cdot5^3\cdot2^6+5^7\cdot2^{10}}{5^6\cdot2^{10}}\)
\(=\dfrac{5^8\cdot2^6-5^7\cdot2^6+5^7\cdot2^{10}}{5^6\cdot2^{10}}\)
\(=\dfrac{5^7\cdot2^6\left(5-1+2^4\right)}{5^6\cdot2^{10}}=\dfrac{5}{16}\cdot\dfrac{20}{1}=\dfrac{100}{16}=\dfrac{25}{4}\)
phá ngoặc ra ta có:
A = 2018/2017 - 2018*2019/1004 - 1/2007 +2
= 1 - 2*(2019 -1)
= 1 - 4016
= -4015
\(\frac{1004}{2007}.\frac{-5}{4}+1004.\frac{-1}{4}-\frac{1004}{2007}.\frac{1}{2}\)
\(=\frac{1004}{2007}.\left(-\frac{5}{4}-\frac{1}{2}\right)+1004.\frac{-1}{4}\)
\(=1004.\frac{1}{2007}.\frac{-7}{4}+1004.\frac{-1}{4}\)
\(=1004.\left(-\frac{7}{8028}+\frac{-1}{4}\right)=1004.\frac{-1007}{2014}=-502\)