Giải phương trình 3-x/2009-2-x/2010+1-x/2011=-1

* Hướng dẫn giải

$$\begin{gathered} \frac{3-x}{2009}-\frac{2-x}{2010}+\frac{1-x}{2011}=-1 \\ \iff \frac{3-x}{2009}+1-\frac{2-x}{2010}-1+\frac{1-x}{2011}+1=0 \\ \iff \frac{2012-x}{2009}-\frac{2012-x}{2010}+\frac{2012-x}{2011}=0 \\ \iff \left(2012-x\right)\left(\frac{1}{2009}-\frac{1}{2010}+\frac{1}{2011}\right)=0 \\ \iff 2012-x=0 (do \frac{1}{2009}-\frac{1}{2010}+\frac{1}{2011}\ne 0) \\ \iff x=2012 \end{gathered}$$