Tinh: 2013/2014+5/2014:5-1/2013
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(\frac{\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}}{\frac{5}{2012}+\frac{5}{2013}-\frac{5}{2014}}-\frac{\frac{2}{2013}+\frac{2}{2014}-\frac{2}{2015}}{\frac{3}{2013}+\frac{3}{2014}-\frac{3}{2015}}\)
=\(\frac{\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}}{5\left(\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}\right)}-\frac{2\left(\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}\right)}{3\left(\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}\right)}=\frac{1}{5}-\frac{2}{3}=\frac{3}{15}-\frac{10}{15}=-\frac{7}{15}\)
\(-2.\frac{-3}{2}.\frac{-4}{3}.\frac{-5}{4}...\frac{-2013}{2012}.\frac{-2014}{2013}\)
\(=-\left(2.\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{2013}{2012}.\frac{2014}{2013}\right)\)(vì dãy trên có 2013 thừa số, mỗi thừa số là âm nên kết quả là âm)
\(=-\frac{2.3.4.5...2013.2014}{2.3.4...2012.2013}\)
\(=-2014\)
\(\frac{-2}{1}.\frac{-3}{2}.\frac{-4}{3}.\frac{-5}{4}.....\frac{-2013}{2012}.\frac{-2014}{2013}\)
\(=\frac{-1}{1}.\frac{-1}{1}.\frac{-1}{1}.....\frac{-1}{1}.\frac{-2014}{1}\)
\(=\frac{2014}{1}=2014\)
Đặt \(\dfrac{1}{5}+\dfrac{2013}{2014}+\dfrac{2015}{2016}=B;\dfrac{2013}{2014}+\dfrac{2015}{2016}+\dfrac{1}{10}=C\)
\(A=\left(B+1\right)\cdot C-B\cdot\left(C+1\right)\)
\(=BC+C-BC-B\)
=C-B
\(=\dfrac{2013}{2014}+\dfrac{2015}{2016}+\dfrac{1}{10}-\dfrac{1}{5}-\dfrac{2013}{2014}-\dfrac{2015}{2016}=-\dfrac{1}{10}\)
\(\frac{2013}{2014}:1\frac{1}{7}+\frac{2013}{2014}:\frac{11}{19}+\frac{2013}{2014}:\frac{11}{5}\)
= \(\frac{2013}{2014}:\left(1\frac{1}{7}+\frac{11}{19}+\frac{11}{5}\right)\)
= \(\frac{2013}{2014}:\left(\frac{8}{7}+\frac{11}{19}+\frac{11}{5}\right)\)
= \(\frac{2013}{2014}:\frac{2608}{665}\)
= \(0,2548...\)
\(\frac{2013}{2014}+\frac{5}{2014}\div5-\frac{1}{2013}\)
\(=\frac{2013}{2014}+\frac{5}{2014}.\frac{1}{5}-\frac{1}{2013}\)
\(=\frac{2013}{2014}+\frac{1}{2014}-\frac{1}{2013}\)
\(=\frac{2014}{2014}-\frac{1}{2013}\)
\(=1-\frac{1}{2013}\)
\(=\frac{2012}{2013}\)