Question

Giải phương trình: \(\frac{2-x_{ }}{2017}-1=\frac{1-x}{2018}-\frac{x}{2019}\)

Answer 1

\(\frac{2-x}{2017}-1=\frac{1-x}{2018}-\frac{x}{2019}\)

\(\Leftrightarrow\) \(\frac{2-x}{2017}+1=\frac{1-x}{2018}+1-\frac{x}{2019}+1\)

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

\(\Leftrightarrow\) \(\frac{2019-x}{2017}-\frac{2019-x}{2018}+\frac{2019-x}{2019}=0\)

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

Mà \(\left(\frac{1}{2017}-\frac{1}{2018}+\frac{1}{2019}\right)\ne0\)

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

\(\Rightarrow\) \(S=\left\{2019\right\}\)