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\(\Leftrightarrow\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+....+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{2009}{2010}\)
\(\Leftrightarrow1-\dfrac{1}{x+1}=\dfrac{2009}{2010}\)
\(\Leftrightarrow-\dfrac{1}{x+1}=-\dfrac{1}{2010}\)
\(\Leftrightarrow x+1=2010\Leftrightarrow x=2009\)
\(\dfrac{x+4}{3}=\dfrac{x-11}{-6}\)
\(\dfrac{2x+8}{6}=\dfrac{-x+11}{6}\)
\(\Leftrightarrow2x+8=-x+11\)
\(\Leftrightarrow3x=3\)
\(\Leftrightarrow x=1\)
\(3,8276< \overline{3,8ab5}< 3,836\)
=>\(276< \overline{ab5}< 360\)
=>\(\left(a,b\right)\in\left\{\left(2;8\right);\left(2;9\right);\left(3;0\right);\left(3;1\right);\left(3;2\right);\left(3;3\right);\left(3;4\right);\left(3;5\right)\right\}\)
\(\dfrac{x-2}{3}=\dfrac{x+5}{4}\\ \Rightarrow4\left(x-2\right)=3\left(x+5\right)\\ \Rightarrow4x-8=3x+15\\ \Rightarrow x-23=0\\ \Rightarrow x=23\)