Giải các phương trình sau a) x-10/2010+x-8/2012+x-6/2014+x-4/2016+x-2/2018=x-2018/2+x-2016/4+x-2014/6+x-2012/8+x-2010/10

* Hướng dẫn giải

$$\begin{gathered} a) \\ \left(\frac{ x-10}{2010}-1\right)+\left(\frac{x-8}{2012}-1\right)+\left(\frac{x-6}{2014}-1\right)+\left(\frac{x-4}{2016}-1\right)+\left(\frac{x-2}{2018}-1\right) \\ =\left(\frac{x-2018}{2}-1\right)+\left(\frac{x-2016}{4}-1\right)+\left(\frac{x- 2014}{6}-1\right)+\left(\frac{x-2012}{8}-1\right)+\left(\frac{x-2010}{/10}-1\right) \\ \iff a)\frac{ x-2020}{2010}+\frac{ x-2020}{2012}+\frac{ x-2020}{2014}+\frac{ x-2020}{2016}+\frac{ x-2020}{2018} \\ =\frac{ x-2020}{2}+\frac{ x-2020}{4}+\frac{ x-2020}{6}+\frac{ x-2020}{8}+\frac{ x-2020}{10} \\ \iff \left( x-2020\right)\left(\frac{ 1}{2010}+\frac{ 1}{2012}+\frac{ 1}{2014}+\frac{1}{2016}+\frac{ 1}{2018} \\ -\frac{ 1}{2}-\frac{ 1}{4}-\frac{1}{6}-\frac{1}{8}-\frac{ 1}{10}\right) \end{gathered}$$