Ta có : \(\frac{x+2015}{5}+\frac{x+2016}{6}=\frac{x+2017}{7}+\frac{x+2018}{8}\)
\(\Rightarrow\frac{x+2015}{5}+\frac{x+2016}{6}-\frac{x+2017}{7}-\frac{x+2018}{8}=0\)
\(\Rightarrow\left(\frac{x+2015}{5}-1\right)+\left(\frac{x+2016}{6}-1\right)-\left(\frac{x+2017}{7}-1\right)-\left(\frac{x+2018}{8}-1\right)=0\)
\(\Leftrightarrow\frac{x+2010}{5}+\frac{x+2010}{6}-\frac{x+2010}{7}-\frac{x+2010}{8}=0\)
\(\Leftrightarrow\left(x+2010\right)\left(\frac{1}{5}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}\right)=0\)
Mà \(\left(\frac{1}{5}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}\right)\ne0\)
\(\Rightarrow x+2010=0\)
=> x = -2010
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