x+1/10+x+1/10=x+1/21
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3 x 15 + 21 x 15 + 85 x 5
= 45 + 315 + 425
= 785
15 - 30 + 40
= 25
21 + 19 - 50 + 10
= 0
\(\dfrac{1}{5}-\dfrac{1}{4}+2\)
\(=-\dfrac{1}{20}+2\)
\(=\dfrac{39}{20}\)
\(\left(\dfrac{1}{4}+\dfrac{1}{6}\right)\times\left(\dfrac{1}{2}-\dfrac{1}{4}\right)\)
\(=\dfrac{5}{12}\times\dfrac{1}{4}\)
\(=\dfrac{5}{12}\times\dfrac{3}{12}\)
\(=\dfrac{5}{48}\)
\(\dfrac{1}{10}+\dfrac{1}{5}-\dfrac{3}{4}\)
\(=-\dfrac{9}{20}\)
\(3\times15+21\times15+85\times5\\ =15\times\left(3+21\right)+425\\ =15\times24+425\\ =360+425\\ =785\)
\(15-30+40\\ =\left(15+40\right)-30\\ =55-30\\ =25\)
\(21+19-50+10\\ =\left(21+19\right)-\left(50-10\right)\\ =40-40\\ =0\)
\(\dfrac{1}{5}-\dfrac{1}{4}+2\)
\(=\dfrac{4}{20}-\dfrac{5}{20}+\dfrac{40}{20}\)
\(=\dfrac{\left(4+40\right)}{20}-\dfrac{5}{20}\)
\(=\dfrac{44}{20}-\dfrac{5}{20}\)
\(=\dfrac{39}{20}\)
\(\left(\dfrac{1}{4}+\dfrac{1}{6}\right)\times\left(\dfrac{1}{2}-\dfrac{1}{4}\right)\)
\(=\dfrac{5}{12}\times\dfrac{1}{4}\)
\(=\dfrac{5}{48}\)
\(\dfrac{1}{10}+\dfrac{1}{5}-\dfrac{3}{4}\)
\(=\dfrac{2}{20}+\dfrac{4}{20}-\dfrac{15}{20}\)
\(=\dfrac{6}{20}-\dfrac{15}{20}\)
\(=-\dfrac{9}{20}\)
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\(x\) + \(\dfrac{1}{10}\) + \(x\) + \(\dfrac{1}{11}\) = \(x\) + \(\dfrac{1}{21}\)
\(x+x-x\) = \(\dfrac{1}{21}\) - \(\dfrac{1}{10}\) - \(\dfrac{1}{11}\)
\(x\) = - \(\dfrac{331}{2310}\)
\(x+\dfrac{1}{10}+x+\dfrac{1}{11}=x+\dfrac{1}{21}\)
\(x+x-x=\dfrac{1}{21}-\dfrac{1}{10}-\dfrac{1}{11}\)
\(x=\dfrac{-11}{210}-\dfrac{1}{11}\)
\(x=\dfrac{-331}{2310}\)
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\(\Leftrightarrow2\left(\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+...+\dfrac{1}{x\left(x+1\right)}\right)=\dfrac{2010}{2012}\)
\(\Leftrightarrow\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{2010}{4024}=\dfrac{1005}{2012}\)
=>1/x+1=-251/1006
=>x+1=-1006/251
=>x=-1257/251
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\(\left(x+1\right)\left(21-1\right)=-21\)
\(\left(x+1\right)\cdot20=-21\)
\(x+1=\frac{-21}{20}\)
\(x=\frac{-21}{20}-1\)
\(x=\frac{-41}{20}\)
( x + 1 ) . ( 21 - 1 ) = -21
( x + 1 ) . 20 = -21
( x + 1 ) = -21 : 20
( x + 1 ) = 1.05
x = 1,05 - 1
x = - 0 ,05
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\(\Rightarrow\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+...+\frac{2}{x.\left(x+1\right)}=\frac{2}{5.6}+\frac{2}{6.7}+\frac{2}{7.8}+\frac{2}{x.\left(x+1\right)}=2.\left(\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{x.\left(x+1\right)}\right)\)
\(=2.\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+1}\right)=2.\left(\frac{1}{5}-\frac{1}{x+1}\right)=\frac{2}{5}-\frac{2}{x+1}=\frac{3}{10}\)
=> \(\frac{2}{x+1}\)= \(\frac{1}{10}=\frac{2}{20}\)
=> x +1 = 20 => x = 19
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![](https://rs.olm.vn/images/avt/0.png?1311)
\(x\) + \(\dfrac{1}{10}\) + \(x\) + \(\dfrac{1}{10}\) = \(x\) + \(\dfrac{1}{21}\)
\(x+x\) - \(x\) = \(\dfrac{1}{21}\) - \(\dfrac{1}{10}\) - \(\dfrac{1}{10}\)
\(x\) = \(\dfrac{1}{21}\) - \(\dfrac{1}{5}\)
\(x\) = - \(\dfrac{16}{105}\)