\(\frac{-1}{2}+\frac{3}{21}+\frac{-2}{6}+\frac{-5}{30}\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{-5}{7}+\frac{3}{4}+\frac{-1}{5}+\frac{-2}{7}+\frac{1}{4}\)
\(A=\left(\frac{-5}{7}+\frac{-2}{7}\right)+\left(\frac{3}{4}+\frac{1}{4}\right)+\frac{-1}{5}\)
\(A=-1+1+\frac{-1}{5}\)
\(A=\frac{-1}{5}\)
\(B=\frac{-4}{12}+\frac{18}{45}+\frac{-6}{9}+\frac{-21}{35}+\frac{6}{30}\)
\(B=\frac{-1}{3}+\frac{2}{5}+\frac{-2}{3}+\frac{-3}{5}+\frac{1}{5}\)
\(B=\left(\frac{-1}{3}+\frac{-2}{3}\right)+\left(\frac{2}{5}+\frac{-3}{5}+\frac{1}{5}\right)\)
\(B=-1+0\)
\(B=-1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(C=\frac{-1}{2}+\frac{3}{21}+\frac{-2}{6}+\frac{-5}{30}\)
\(C=\frac{-1}{2}+\frac{1}{7}+\frac{-1}{3}+\frac{1}{6}\)
\(C=\frac{-21}{42}+\frac{6}{42}+\frac{-14}{42}+\frac{7}{42}\)
\(C=\frac{-22}{42}\)
\(\Rightarrow C=\frac{-11}{21}\)
Vậy \(C=\frac{-11}{21}\)
C=\(\frac{-105}{210}+\frac{30}{210}+\frac{-70}{210}+\frac{-35}{210}=\frac{\left(-105\right)+30+\left(-70\right)+\left(-35\right)}{210}=\frac{-180}{210}=\frac{-6}{7}\)
Tự rút gọn!
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{5}{12}+\frac{5}{20}+\frac{5}{30}+...+\frac{5}{9900}=\frac{5}{3.4}+\frac{5}{4.5}+\frac{5}{5.6}+...+\frac{5}{99.100}\)
\(5\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(5\left(\frac{1}{3}-\frac{1}{100}\right)=\frac{97}{60}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{-1}{2}+\frac{1}{3}+\frac{2}{4}=\frac{-6}{12}+\frac{4}{12}+\frac{6}{12}\)
= \(\frac{4}{12}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
b) \(\frac{\frac{2}{3}+\frac{5}{7}+\frac{4}{21}}{\frac{5}{6}+\frac{11}{7}-\frac{7}{21}}\)
\(=\frac{\frac{29}{21}+\frac{4}{21}}{\frac{101}{42}-\frac{7}{21}}\)
\(=\frac{\frac{11}{7}}{\frac{29}{14}}\)
\(=\frac{22}{29}.\)
Chúc bạn học tốt!
![](https://rs.olm.vn/images/avt/0.png?1311)
c) x=-2 nha
d) =\(\frac{1}{5.6}\)+\(\frac{1}{6.7}\)+......+\(\frac{1}{11.12}\)
=\(\frac{1}{5}\)-\(\frac{1}{6}\)+\(\frac{1}{6}\)-\(\frac{1}{7}\)+.....+\(\frac{1}{11}\)-\(\frac{1}{12}\)
=\(\frac{1}{5}\)-\(\frac{1}{12}\)= \(\frac{7}{60}\)
\(\frac{-1}{2}+\frac{3}{21}+\frac{-2}{6}+\frac{-5}{30}\)
\(\frac{-1}{2}+\frac{1}{7}+\frac{-1}{3}+\frac{-1}{6}\)
\(\frac{-21}{42}+\frac{6}{42}+\frac{-14}{42}+\frac{-7}{42}\)
\(\frac{-36}{42}=-\frac{6}{7}\)