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\(\frac{x}{2}-\left(\frac{3}{5}x-\frac{13}{5}\right)=-\left(\frac{7}{5}+\frac{7}{10}x\right)\)
\(\Rightarrow\frac{5x-6x+26+14+7x}{10}=0\Rightarrow6x+40=0\Rightarrow x=-\frac{20}{3}\)
Chắc bạn gõ nhầm số hạng thứ 3 phải là +5/7.
Tổng này đối xứng qua 13/15. Các đối xứng trái dấu nên Tổng = 13/15
a) \(\frac{7}{15}+\frac{9}{10}+\frac{8}{15}-\frac{-1}{10}-\frac{20}{10}+\frac{1}{157}\)
\(=\frac{7}{15}+\frac{9}{10}+\frac{8}{15}+\frac{1}{10}-\frac{20}{10}+\frac{1}{157}\)
\(=\left(\frac{7}{15}+\frac{8}{15}\right)+\left(\frac{9}{10}+\frac{1}{10}\right)-2+\frac{1}{157}\)
\(=1+1-2+\frac{1}{157}\)
\(=2-2+\frac{1}{157}\)
\(=0+\frac{1}{157}=\frac{1}{157}\)
b) \(\frac{1}{13}+\frac{16}{7}+\frac{3}{105}-\frac{9}{7}-\frac{-12}{13}\)
\(=\frac{1}{13}+\frac{16}{7}+\frac{1}{35}-\frac{9}{7}+\frac{12}{13}\)
\(=\left(\frac{1}{13}+\frac{12}{13}\right)+\left(\frac{16}{7}-\frac{9}{7}\right)+\frac{1}{35}\)
\(=1+1+\frac{1}{35}\)
\(=2+\frac{1}{35}\)
\(=\frac{70}{35}+\frac{1}{35}=\frac{71}{35}\)
\(B=\frac{1}{5}-\frac{3}{7}+\frac{5}{9}-\frac{2}{11}+\frac{7}{13}-\frac{9}{16}-\frac{7}{13}+\frac{2}{12}-\frac{5}{9}+\frac{3}{7}-\frac{1}{5}-\frac{1}{5}\)
\(B=\left(\frac{1}{5}-\frac{1}{5}\right)-\left(\frac{3}{7}-\frac{3}{7}\right)+\left(\frac{5}{9}-\frac{5}{9}\right)+\left(\frac{7}{13}-\frac{7}{13}\right)-\frac{2}{11}+\frac{2}{12}-\frac{9}{16}-\frac{1}{5}\)
\(B=0-0+0+0-\frac{2}{11}+\frac{2}{12}-\frac{9}{16}-\frac{1}{5}\)
\(B=\frac{-2}{11}+\frac{2}{12}-\frac{9}{16}-\frac{1}{5}\)
Đến đây chỉ còn cách quy đồng thôi
\(5.\left|-\frac{1}{10}+\frac{7}{15}\right|-\frac{2}{13}.4\frac{1}{3}\)
\(=5.\left|-\frac{3}{30}+\frac{14}{30}\right|-\frac{2}{13}.\frac{13}{3}\)
\(=5.\left|\frac{11}{30}\right|-\frac{2}{3}\)
\(=5.\frac{11}{30}-\frac{20}{30}\)
\(=\frac{55}{30}-\frac{20}{30}\)
\(=\frac{35}{30}=\frac{7}{6}\)hoặc \(1\frac{1}{6}\)
= 1/3 - 1/3 + 5/7 - 5/7 - 7/9 + 7/9 +9/11 - 9/11 -11/13 + 11/13 +13/15
= 0 + 0 - 0 + 0 -0 + 13/15
= 0 + 13/15
= 13/15
\(\frac{1}{3}-\frac{3}{5}+\frac{5}{7}-\frac{7}{9}+\frac{9}{11}-\frac{11}{13}+\frac{13}{15}+\frac{11}{13}-\frac{9}{11}+\frac{7}{9}-\frac{5}{7}+\frac{3}{5}-\frac{1}{3}\)
\(=\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{3}{5}-\frac{3}{5}\right)+\left(\frac{5}{7}-\frac{5}{7}\right)+\left(\frac{7}{9}-\frac{7}{9}\right)+\left(\frac{9}{11}-\frac{9}{11}\right)+\left(\frac{11}{13}-\frac{11}{13}\right)+\frac{13}{15}\)
\(=0+0+0+0+0+0+\frac{13}{15}\)
\(=\frac{13}{15}\)
\(\frac{1}{7}.\frac{15}{13}+\frac{5}{13}.\frac{12}{7}-\frac{1}{7}.\frac{10}{3}\)
=\(\frac{1}{7}.\frac{15}{13}+\frac{1}{7}.\frac{5}{13}.12-\frac{1}{7}.\frac{10}{3}\)
=\(\frac{1}{7}\left(\frac{15}{13}+\frac{60}{13}+\frac{10}{3}\right)\)
=\(\frac{1}{7}\left(\frac{75}{13}-\frac{10}{3}\right)=\frac{1}{7}.\left(\frac{75.3-13.10}{39}\right)=\frac{1}{7}.\frac{95}{39}\)
=\(\frac{95}{273}\)
\(\frac{1}{7}.\frac{15}{13}+\frac{5}{13}.\frac{12}{7}-\frac{1}{7}.\frac{10}{3}\)
= \(\frac{1}{7}.\frac{15}{13}+\frac{5.12}{13}.\frac{1}{7}-\frac{1}{7}.\frac{10}{3}\)
= \(\frac{1}{7}.\left(\frac{15}{13}+\frac{60}{13}\right)-\frac{1}{7}.\frac{10}{3}\)
= \(\frac{1}{7}.\frac{75}{13}-\frac{10}{21}\)
= \(\frac{75}{91}-\frac{10}{21}\)
= \(\frac{95}{273}\)