Question

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

Answer 1

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

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

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

\(\Leftrightarrow\frac{x+2017}{2013}+\frac{x+2017}{2014}-\frac{x+2017}{2015}-\frac{x+2017}{2016}=0\)

\(\Leftrightarrow\left(x+2017\right)\left(\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}-\frac{1}{2016}\right)=0\)

\(\Leftrightarrow x+2017=0\) ( vì \(\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}-\frac{1}{2016}\)>0)

\(\Leftrightarrow x=2017\)

Answer 2

thank nha

>3