Question

giải pt: 

(x+1)/2018 - (x+2)/2017 = (x+3)/2016       +1

Answer 1

\(\frac{x+1}{2018}-\frac{x+2}{2017}=\frac{x+3}{2016}+1\)

\(\Leftrightarrow\frac{x+1}{2018}+1-\left(\frac{x+2}{2017}+1\right)=\frac{x+3}{2016}+1\)

\(\Leftrightarrow\frac{x+2019}{2018}-\frac{x+2019}{2017}=\frac{x+2019}{2016}\)

\(\Leftrightarrow\left(x+2019\right)\left(\frac{1}{2018}-\frac{1}{2017}-\frac{1}{2016}\right)=0\)

Có: \(\frac{1}{2018}-\frac{1}{2017}-\frac{1}{2016}\ne0\)

\(\Leftrightarrow x+2019=0\Leftrightarrow x=-2019\)

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