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\(\frac{11}{13}-\left(\frac{5}{42}-x\right)=-\left(\frac{15}{28}-\frac{11}{13}\right)\)
\(\left(\frac{5}{42}-x\right)=\frac{11}{13}-\left(-\frac{15}{28}-\frac{11}{13}\right)\)
\(\frac{5}{42}-x\)= \(\frac{11}{13}-\left(-\frac{503}{364}\right)\)
\(\frac{5}{42}-x\)= \(\frac{811}{364}\)
\(x=\frac{5}{42}-\frac{811}{364}\)
\(x=-\frac{329}{156}\)
Phần tìm x tự tính ra
\(D=\frac{1}{3}-\frac{3}{5}+\frac{5}{7}-\frac{7}{9}+\frac{9}{11}-\frac{11}{13}+\frac{13}{15}+\frac{11}{13}-\frac{9}{11}+\frac{7}{9}-\frac{5}{7}+\frac{3}{5}-\frac{1}{3}\)
\(D=\left(\frac{1}{3}-\frac{1}{3}\right)-\left(\frac{3}{5}-\frac{3}{5}\right)+\left(\frac{5}{7}-\frac{5}{7}\right)-\left(\frac{7}{9}-\frac{7}{9}\right)+\left(\frac{9}{11}-\frac{9}{11}\right)-\left(\frac{11}{13}-\frac{11}{13}\right)+\frac{13}{15}\)
\(D=0+\frac{13}{15}=\frac{13}{15}\)
\(\frac{11}{13}-\left(\frac{5}{42}-x\right)=-\left(\frac{5}{28}-\frac{11}{13}\right)\)
\(\frac{11}{13}-\frac{5}{42}+x=-\frac{5}{28}+\frac{11}{13}\)
\(x=-\frac{5}{28}+\frac{11}{13}-\frac{11}{13}+\frac{5}{42}\)
\(x=\left(\frac{11}{13}-\frac{11}{13}\right)-\left(\frac{5}{28}-\frac{5}{42}\right)\)
\(x=-\left(\frac{15}{84}-\frac{10}{84}\right)\)
\(x=-\frac{5}{84}\)
B. 1/3 - 1/3 - 3/5 +3/5 + 5/7 - 5/7 + 9/11 - 9/11 -11/13 + 11/ 13 + 7/9 + 13/15
= 0 -0-0-0-0+7/9 +13/15
= 74/45
\(\Leftrightarrow\frac{11}{13}-\frac{5}{42}+x=-\left(-\frac{113}{364}\right)\)
\(\Leftrightarrow\frac{397}{546}+x=\frac{113}{364}\)
\(\Leftrightarrow x=\frac{113}{364}-\frac{397}{546}=-\frac{5}{12}\)
\(\Rightarrow\frac{5}{42}-x=\frac{11}{13}+\left(\frac{15}{28}-\frac{11}{13}\right)\)
\(\Rightarrow\frac{5}{42}-x=\frac{15}{28}\)
\(\Rightarrow x=\frac{5}{42}-\frac{15}{28}=-\frac{5}{12}\)