Question

Giải Phương trình;

\(\frac{2-x}{2005}-1=\frac{1-x}{2006}-\frac{x}{2007}\)

giúp mk nhé

Answer 1

Có : \(\frac{2-x}{2005}-1\) = \(\frac{1-x}{2006}-\frac{x}{2007}\)

\(\Leftrightarrow\) \(\frac{2-x}{2005}+1=\left(\frac{1-x}{2006}+1\right)-\left(\frac{x}{2007}+1\right)\)

\(\Leftrightarrow\) \(\frac{-x+2007}{2005}=\frac{-x+2007}{2006}+\frac{-x+2007}{2007}\)

\(\Leftrightarrow\) \(\left(-x+2007\right)\left(\frac{1}{2005}-\frac{1}{2006}-\frac{1}{2007}\right)=0\)

\(\Leftrightarrow\) \(-x+2007=0\) ( vì \(\left(\frac{1}{2005}-\frac{1}{2006}-\frac{1}{2007}\right)\ne0\)

\(\Leftrightarrow\) \(x=2007\)

Vậy \(x=2007\)