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a; \(\dfrac{1}{2}-\dfrac{-3}{6}+\dfrac{5}{3}-\dfrac{9}{12}\)
\(=\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{5}{3}-\dfrac{3}{4}\)
\(=1-\dfrac{3}{4}+\dfrac{5}{3}=\dfrac{1}{4}+\dfrac{5}{3}=\dfrac{3+20}{12}=\dfrac{23}{12}\)
b: \(=\dfrac{3}{11}\left(-\dfrac{2}{3}+\dfrac{-16}{9}\right)\)
\(=\dfrac{3}{11}\cdot\dfrac{-6-16}{9}=\dfrac{3}{11}\cdot\dfrac{-22}{9}=\dfrac{-2}{3}\)
c: \(=1-3+\dfrac{1}{4}=-2+\dfrac{1}{4}=-\dfrac{7}{4}\)
1.
\(\dfrac{2}{3}.\left\{\dfrac{2}{3}-\dfrac{2}{3}.\left[\dfrac{2}{3}-\dfrac{2}{3}.\left(\dfrac{2}{3}-\dfrac{1}{2}\right)\right]\right\}\)
=\(\dfrac{2}{3}.\left\{\dfrac{2}{3}-\dfrac{2}{3}.\left[\dfrac{2}{3}-\dfrac{2}{3}.\dfrac{1}{6}\right]\right\}\)
=\(\dfrac{2}{3}.\left\{\dfrac{2}{3}-\dfrac{2}{3}.\left[\dfrac{2}{3}-\dfrac{1}{9}\right]\right\}\)
=\(\dfrac{2}{3}.\left\{\dfrac{2}{3}-\dfrac{2}{3}.\dfrac{5}{9}\right\}\)
=\(\dfrac{2}{3}.\left\{\dfrac{2}{3}-\dfrac{10}{27}\right\}\)
=\(\dfrac{2}{3}.\dfrac{8}{27}\)
=...
\(A=6-\dfrac{2}{3}+\dfrac{1}{3}-5-\dfrac{5}{7}+\dfrac{3}{2}-3+\dfrac{7}{3}-\dfrac{5}{2}\)
\(A=\left(6-5-3\right)+\left(\dfrac{1}{3}-\dfrac{2}{3}+\dfrac{7}{3}\right)+\left(\dfrac{3}{2}-\dfrac{5}{2}\right)-\dfrac{5}{7}\)
\(A=-2+2-1-\dfrac{5}{7}\)
\(A=-1\dfrac{5}{7}\)
Đề ảo tek.Sửa đề.
\(\left\{{}\begin{matrix}a+b+c=5\\\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(a+b+c\right)^2=25\\\dfrac{bc}{abc}+\dfrac{ac}{abc}+\dfrac{ab}{abc}=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}a^2+b^2+c^2+2ab+2bc+2ac=25\\bc+ac+ab=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}a^2+b^2+c^2+2ab+2bc+2ac=25\\2bc+2ac+2ab=0\end{matrix}\right.\)
\(\Leftrightarrow a^2+b^2+c^2+2ab-2ab+2bc-2bc+2ac-2ac=25\)
\(\Leftrightarrow a^2+b^2+c^2=25\)
(\(\dfrac{5}{7}\)-\(\dfrac{7}{5}\))-[\(\dfrac{1}{2}\)-(\(\dfrac{-2}{7}\)-\(\dfrac{1}{10}\))]
=(\(\dfrac{25}{35}\)-\(\dfrac{49}{35}\))-[\(\dfrac{1}{2}\)-(\(\dfrac{-20}{70}\)-\(\dfrac{7}{70}\))
=\(\dfrac{-24}{35}\)-[\(\dfrac{1}{2}\)-(\(\dfrac{-27}{70}\))]
=\(\dfrac{-24}{35}\)-\(\dfrac{31}{35}\)
=\(\dfrac{-55}{35}\)
=\(\dfrac{-11}{7}\)