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a, \(\left(31\frac{6}{13}+5\frac{9}{41}\right)-36\frac{6}{13}=31\frac{6}{16}+5\frac{9}{41}-36\frac{6}{13}\)
\(=\left(31\frac{6}{16}-31\frac{6}{16}\right)+5\frac{9}{41}\)
\(=0+5\frac{9}{41}=5\frac{9}{41}\)
b, \(\left(17\frac{29}{31}-3\frac{7}{8}\right)-\left(2\frac{28}{31}-4\right)=17\frac{9}{31}-3\frac{7}{8}-2\frac{28}{31}+4\)
Ta có :
Đặt \(A=\frac{31}{3}+\frac{31}{15}+...+\frac{31}{143}\)
\(A=\frac{31}{1.3}+\frac{31}{3.5}+...+\frac{31}{11.13}\)
\(\frac{2}{31}A=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{11.13}\)
\(\frac{2}{31}A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}\)
\(\frac{2}{31}A=1-\frac{1}{13}\)
\(A=\frac{12}{13}:\frac{2}{31}\)
\(A=\frac{186}{13}\)
\(\Rightarrow x-\frac{186}{13}=\frac{9}{13}\)
\(x=\frac{9}{13}+\frac{186}{13}\)
\(x=\frac{195}{13}=15\)
Ủng hộ mk nha !!! ^_^
\(\text{Đặt }A=\frac{31}{3}+\frac{31}{15}+...+\frac{31}{143}\)
\(\Rightarrow A=\frac{31}{1.3}+\frac{31}{3.5}+...+\frac{31}{11.13}\)
\(\Rightarrow\frac{2}{31}A=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{11.13}\)
\(\Rightarrow\frac{2}{31}A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}\)
\(\Rightarrow\frac{2}{31}A=1-\frac{1}{13}\Rightarrow A=\frac{12}{13}:\frac{2}{31}=\frac{186}{13}\)
\(\Rightarrow x-\frac{186}{13}=\frac{9}{13}\)
\(\Rightarrow x=\frac{9}{13}+\frac{186}{13}\)
\(\Rightarrow x=\frac{195}{13}=15\)
\(17\frac{2}{31}-\left(\frac{15}{17}+6\frac{2}{31}\right)\)
\(17\frac{2}{31}=\frac{529}{31};6\frac{2}{31}=\frac{188}{31}\)
\(17\frac{2}{31}-\left(\frac{15}{17}+6\frac{2}{31}\right)\)
\(=\frac{529}{31}-\left(\frac{15}{17}+\frac{188}{31}\right)\)
\(=\frac{529}{31}-\frac{3661}{527}\)
\(=\frac{172}{17}\)
\(\left(\frac{29}{31}-\frac{7}{8}\right)-\left(\frac{28}{31}-4\right)\)
\(=\frac{15}{248}-\left(-\frac{96}{31}\right)\)
\(=\frac{783}{248}\)
\(C=9\cdot\left(\frac{\frac{26299}{2023}-\frac{3757}{2023}-\frac{91}{2023}}{\frac{8092}{2023}-\frac{1156}{2023}-\frac{28}{2023}}\right):\left(\frac{\frac{840255}{21545}+\frac{168051}{21545}+\frac{6045}{21545}+\frac{27105}{21545}}{\frac{344720}{21545}+\frac{68944}{21545}+\frac{2480}{21545}+\frac{11120}{21545}}\right)\cdot\frac{158158}{164164}\)
\(C=9\cdot\left(\frac{\frac{22451}{2023}}{\frac{6908}{2023}}\div\frac{\frac{1041456}{21545}}{\frac{427264}{21545}}\right)\cdot\frac{158158}{164164}\)
\(C=9\cdot\left(\frac{13}{4}\div\frac{39}{16}\right)\cdot\frac{158158}{164164}\)
\(C=9\cdot\frac{4}{3}\cdot\frac{2\cdot79\cdot2\cdot79}{2\cdot82\cdot2\cdot82}=9\cdot\frac{4}{3}\cdot\frac{79}{82}\)
\(C=\frac{474}{41}\)
\(X-\left(\frac{31}{5}+\frac{31}{15}+\frac{31}{35}+\frac{31}{63}+\frac{31}{99}+\frac{31}{143}\right)=\frac{9}{13}\)
\(X-\left(\frac{31}{5}+\frac{31}{3\cdot5}+\frac{31}{5\cdot7}+\frac{31}{7\cdot9}+\frac{31}{9\cdot11}+\frac{31}{11\cdot13}\right)=\frac{9}{13}\)
\(X-\left[\frac{31}{2}\cdot\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)+\frac{31}{5}\right]=\frac{9}{13}\)
\(X-\left[\frac{31}{2}\cdot\left(\frac{1}{3}-\frac{1}{13}\right)+\frac{31}{5}\right]=\frac{9}{13}\)
\(X-\left[\frac{31}{2}\cdot\frac{10}{39}+\frac{31}{5}\right]=\frac{9}{13}\)
\(X-\frac{1984}{195}=\frac{9}{13}\)
\(\Rightarrow X=\frac{9}{13}+\frac{1984}{195}=\frac{163}{15}\)
163 / 15
mk nghĩ v