\(\frac{x-1}{2016}+\frac{x-2}{2015}-\frac{x-3}{2014}=\frac{x-4}{2013}\)
\(\left(\frac{x-1}{2016}-1\right)+\left(\frac{x-2}{2015}-1\right)-\left(\frac{x-3}{2014}-1\right)-\left(\frac{x-4}{2013}-1\right)=0\)
\(\frac{x-2017}{2016}+\frac{x-2017}{2015}-\frac{x-2017}{2014}-\frac{x-2017}{2013}=0\)
\(\left(x-2017\right)\left(\frac{1}{2016}+\frac{1}{2015}-\frac{1}{2014}-\frac{1}{2013}\right)=0\)
\(x-2017=0\left(\frac{1}{2016}+\frac{1}{2015}-\frac{1}{2014}-\frac{1}{2013}\ne0\right)\)
\(x=2017\)
x-1/2016+x-2/2015-x-3/2014=x-4/2013
<=> x-1/2016+x-2/2015-x-3/2014-x-4/2013=0
trừ mỗi phân số thêm 1 ta được
x-2017/2016+x-2017/2015-x-2017/2014-x-2017/2013=0
<=>(x-2017).(1/2016+1/2015+1/2014+1/2013)=0
(1/2016+1/2015+1/2014+1/2013) khác 0
=>x-2017=0
<=>x=2017
vậy x = 2017
