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a ) \(\frac{2016\cdot12+2003+2000\cdot2015+2015}{2015+2015\cdot502+504\cdot2015}\)
\(=\frac{\left(2015+1\right)\cdot12+2003+2000\cdot2015+2015}{2015\cdot\left(1+502+504\right)}\)
\(=\frac{2015\cdot12+12\cdot1+2003+2000\cdot2015+2015}{2015\cdot1007}\)
\(=\frac{2015\cdot12+\left(12\cdot1+2003\right)+2000\cdot2015+2015}{2015\cdot1007}\)
\(=\frac{2015\cdot12+2015+2000\cdot2015+2015}{2015\cdot1007}\)
\(=\frac{2015\cdot\left(12+1+2000+1\right)}{2015\cdot1007}\)
\(=\frac{2015\cdot2014}{2015\cdot1007}\)
\(=2\)
b ) \(\frac{1978\cdot1979+1980\cdot21+1958}{1980\cdot1979-1978\cdot1979}\)
\(=\frac{1978\cdot1979+\left(1979+1\right)\cdot21+1958}{\left(1980-1978\right)\cdot1979}\)
\(=\frac{1979\cdot1978+1979\cdot21+21\cdot1+1958}{2\cdot1979}\)
\(=\frac{1978\cdot1979+1979\cdot21+1979}{2\cdot1979}\)
\(=\frac{\left(1978+21+1\right)\cdot1979}{2\cdot1979}\)
\(=\frac{2000\cdot1979}{2\cdot1979}\)
\(=1000\)
\(=\frac{2013\cdot2015+2015-1}{2015\cdot2013+2014}\)
\(=\frac{2015\cdot2013+\left(2015-1\right)}{2015\cdot2013+2014}\)
\(=\frac{2015\cdot2013+2014}{2015\cdot2013+2014}\)
\(=1.\)
Vậy.........
a,\(\frac{2015.2016+2015-1}{2014+2015.2016}=\frac{2015.2016+2014}{2014+2015.2016}=1\)\(1\)
b,\(=1-\frac{1}{5}+\frac{1}{5}...-\frac{1}{2011}+\frac{1}{2011}-\frac{1}{2015}=1-\frac{1}{2015}=\frac{2014}{2015}\)
c,\(=\frac{12}{35}+\frac{12}{35}+\frac{12}{35}+\frac{12}{35}=\frac{12}{35}.4=\frac{48}{35}\)
\(\left(2013.2014+2014.2015+2015.2016\right)\left(1+\frac{1}{3}-1\frac{1}{3}\right)\)
\(=\left(2013.2014+2014.2015+2015.2016\right)\left(\frac{4}{3}-\frac{4}{3}\right)\)
\(=\left(2013.2014+2014.2015+2015.2016\right).0\)
\(=0\)
a ) ( 1978 x 1979 + 1980 x 21 + 1958 ) / ( 1980 x 1979 - 1978 x 1979 ) = 1978 x 1979 + 1980 / 1979 . ( 1980 - 1978 )
= 0/1979