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\(1,-\frac{1}{5}x-\frac{2}{3}=\frac{1}{10}x+\frac{5}{6}\)
\(-\frac{1}{5}x-\frac{2}{3}-\frac{1}{10}x-\frac{5}{6}=0\)
\(-\frac{3}{10}x-\frac{3}{2}=0\)
\(-\frac{3}{10}x=\frac{3}{2}\)
\(x=-5\)
\(2,2\left(x-\frac{1}{3}\right)-3\left(x-\frac{1}{2}\right)=\frac{1}{2}x\)
\(x-\frac{2}{3}-3x+\frac{3}{2}=\frac{1}{2}x\)
\(-2x+\frac{5}{6}=\frac{1}{2}x\)
\(-2x-\frac{1}{2}x+\frac{5}{6}=0\)
\(-\frac{5}{2}x=-\frac{5}{6}\)
\(x=\frac{1}{3}\)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2014}{2015}\)
\(\Rightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2014}{2015}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{1007}{2015}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{1007}{2015}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{4030}\)
=>x+1=4030
=>x=4029
vậy x=4029
\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2013}{2015}\)
\(2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2013}{2015}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2013}{2015}:2\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2013}{4030}\)
tự làm tiếp nhé mk ăn cơm đã