Tính
a) 8/21+13/21
b) 5/6:-7/12
c) -4 và 1/4 - 3/4
d) 7/9x8/17+7/9x15/17-7/9x6/17
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AM-GM:\(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2010}\ge4\sqrt[4]{\frac{2010.2011.2012.2013}{2011.2012.2013.2010}}=4\sqrt[4]{1}=4\)
\(\Rightarrow S\ge4\)
^^
Ta có \(B=\frac{2015+2016+2017}{2016+2017+2018}\)
\(\Leftrightarrow B=\frac{2015}{2016+2017+2018}+\frac{2016}{2016+2017+2018}+\frac{2017}{2016+2017+2018}\)
Vì
\(\frac{2015}{2016}>\frac{2015}{2016+2017+2018};\frac{2016}{2017}>\frac{2016}{2016+2017+2018};\frac{2017}{2018}>\frac{2017}{2016+2017+2018}\) nên \(\frac{2015}{2016}+\frac{2016}{2017}+\frac{2017}{2018}>\frac{2015}{2016+2017+2018}+\frac{2016}{2016+2017+2018}+\frac{2017}{2016+2017+2018}\)
Hay \(A>B\)
a) \(\frac{8}{21}+\frac{13}{21}=\frac{8+13}{21}=\frac{21}{21}=1\)
b) \(\frac{5}{6}:\frac{-7}{12}=\frac{5}{6}.\frac{12}{-7}=\frac{10}{-7}\)
c) \(-4\frac{1}{4}-\frac{3}{4}=\frac{-17}{4}-\frac{3}{4}=\frac{-17-3}{4}=\frac{-20}{4}=-5\)
d) \(\frac{7}{9}.\frac{8}{17}+\frac{7}{9}.\frac{15}{17}-\frac{7}{9}.\frac{6}{17}\)
\(=\frac{7}{9}.\left(\frac{8}{17}+\frac{15}{17}-\frac{6}{17}\right)\)
\(=\frac{7}{9}.\frac{17}{17}\)
\(=\frac{7}{9}.1\)
\(=\frac{7}{9}\)
a) \(\frac{8}{21}+\frac{13}{21}=1\)
b) \(\frac{5}{6}\div\frac{-7}{12}=\frac{5}{6}.\frac{-12}{7}=\frac{-10}{7}\)
c) \(-4\frac{1}{4}-\frac{3}{4}=\frac{-17}{4}-\frac{3}{4}=-5\)
d) \(\frac{7}{9}.\frac{8}{17}+\frac{7}{9}.\frac{15}{7}-\frac{7}{9}.\frac{6}{17}=\frac{7}{9}.\left(\frac{8}{17}+\frac{15}{17}-\frac{6}{17}\right)=\frac{7}{9}.1=\frac{7}{9}\)