Question

giải phương trình

(2-x)/2013-1=(1-x)/2014-x/2015

Answer 1

\(\dfrac{2-x}{2013}-1=\dfrac{1-x}{2014}-\dfrac{x}{2015}\)

\(\Leftrightarrow\dfrac{2-x+2013}{2013}-1+1=\dfrac{1-x+2014}{2014}+\dfrac{-x+2015}{2015}\) (Cộng 2 vế cho 1+1)

\(\Leftrightarrow\dfrac{2015-x}{2013}=\dfrac{2015-x}{2014}+\dfrac{2015-x}{2015}\)

\(\Leftrightarrow\dfrac{2015-x}{2013}-\dfrac{2015-x}{2014}-\dfrac{2015-x}{2015}=0\)

\(\Leftrightarrow\left(2015-x\right)\left(\dfrac{1}{2013}-\dfrac{1}{2014}-\dfrac{1}{2015}\right)=0\)

\(\Leftrightarrow2015-x=0\) (Vì \(\dfrac{1}{2013}-\dfrac{1}{2014}-\dfrac{1}{2015}\ne0\))

\(\Leftrightarrow x=2015\)

Vậy phương trình có tập nghiệm là x = 2015