Question

[Phạm Hà My]

\(\frac{x}{2012}\) + \(\frac{x+1}{2013}\) +\(\frac{x+2}{2014}\)+\(\frac{x+3}{2015}\) +\(\frac{x+4}{2016}\) =5

Answer 1

[Nguyễn Việt Lâm]

\(\Leftrightarrow\frac{x}{2012}-1+\frac{x+1}{2013}-1+\frac{x+2}{2014}-1+\frac{x+3}{2015}-1+\frac{x+4}{2016}-1=0\)

\(\Leftrightarrow\frac{x-2012}{2012}+\frac{x-2012}{2013}+\frac{x-2012}{2014}+\frac{x-2012}{2015}+\frac{x-2012}{2016}=0\)

\(\Leftrightarrow\left(x-2012\right)\left(\frac{1}{2012}+\frac{1}{2013}+\frac{1}{2014}+\frac{1}{2015}+\frac{1}{2016}\right)=0\)

\(\Leftrightarrow x=2012\)