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a) Ta có: \(\dfrac{-5}{7}\left(\dfrac{14}{5}-\dfrac{7}{10}\right):\left|-\dfrac{2}{3}\right|-\dfrac{3}{4}\left(\dfrac{8}{9}+\dfrac{16}{3}\right)+\dfrac{10}{3}\left(\dfrac{1}{3}+\dfrac{1}{5}\right)\)
\(=\dfrac{-5}{7}\cdot\dfrac{3}{2}\cdot\dfrac{21}{10}-\dfrac{3}{4}\cdot\dfrac{56}{3}+\dfrac{10}{3}\cdot\dfrac{8}{15}\)
\(=\dfrac{-9}{4}-14+\dfrac{16}{9}\)
\(=\dfrac{-1621}{126}\)
b) Ta có: \(\dfrac{17}{-26}\cdot\left(\dfrac{1}{6}-\dfrac{5}{3}\right):\dfrac{17}{13}-\dfrac{20}{3}\left(\dfrac{2}{5}-\dfrac{1}{4}\right)+\dfrac{2}{3}\left(\dfrac{6}{5}-\dfrac{9}{2}\right)\)
\(=\dfrac{-17}{26}\cdot\dfrac{13}{17}\cdot\dfrac{-3}{2}-\dfrac{20}{3}\cdot\dfrac{3}{20}+\dfrac{2}{3}\cdot\dfrac{-33}{10}\)
\(=\dfrac{3}{4}-1-\dfrac{11}{5}\)
\(=-\dfrac{49}{20}\)
\(a,7\frac{5}{9}-\left(2\frac{3}{4}+3\frac{5}{9}\right)\)
\(=\frac{68}{9}-\frac{11}{4}-\frac{32}{9}\)
\(=4-\frac{11}{4}\)
\(=\frac{5}{4}\)
\(b,\left[\frac{3}{5}.\left(\frac{-7}{10}\right)+\frac{2}{10}.\frac{3}{5}\right]:\left(-3\right)\)
\(=\left(\frac{-21}{50}+\frac{3}{25}\right):\left(-3\right)\)
\(=\frac{-3}{10}:\left(-3\right)\)
\(=\frac{1}{10}\)
Bạn tham khảo tại đây nhé: Câu hỏi của Nguyễn Chí Thành.
Chúc bạn học tốt!
\(A=\frac{1+5+5^2+...+5^{10}}{1+5+5^2+...+5^9}=\frac{1+5\left(1+5+5^2+...+5^9\right)}{1+5+5^2+...+5^9}=\frac{1}{1+5+5^2+...+5^9}+5\)
\(B=\frac{1+3+...+3^{10}}{1+3+...+3^9}=\frac{1+3\left(1+3+...+3^9\right)}{1+3+...+3^9}=\frac{1}{1+3+...+3^9}+3\)
\(\Rightarrow A>B\)
\(\dfrac{3^8\cdot20^5-3^9\cdot5^5\cdot2^9}{6^8\cdot10^4-3^8\cdot2^9\cdot5^4}=\dfrac{3^8\cdot2^{10}\cdot5^5-3^9\cdot5^5\cdot2^9}{2^8\cdot3^8\cdot2^4\cdot5^4-3^8\cdot2^9\cdot5^4}\\ =\dfrac{3^8\cdot2^9\cdot5^5\left(2-3\right)}{2^9\cdot3^8\cdot5^4\left(2^3-1\right)}=\dfrac{-5}{2^3-1}=\dfrac{-5}{7}\)
\(\frac{3}{10}.\left(\frac{-5}{9}+\frac{3}{5}\right)-\frac{3}{10}.\left(\frac{3}{9}-\frac{2}{5}\right)\)
\(=\frac{3}{10}.\frac{2}{45}-\frac{3}{10}.\frac{-3}{45}\)
\(=\frac{3}{10}.\left(\frac{2}{45}-\frac{-3}{45}\right)\)
\(=\frac{3}{10}.\frac{1}{9}\)
\(=\frac{1}{30}\)
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