x 5/2015 x 6/2014=x 7/2013 x 8/2012

Lời giải:

\(\frac{{x + 5}}{{2015}} + \frac{{x + 6}}{{2014}} + \frac{{x + 7}}{{2013}} + \frac{{x + 8}}{{2012}} + \frac{{x + 9}}{{2011}} = - 5\)

⇔\(\frac{{x + 5}}{{2015}} + \frac{{x + 6}}{{2014}} + \frac{{x + 7}}{{2013}} + \frac{{x + 8}}{{2012}} + \frac{{x + 9}}{{2011}} + 5 = 0\)

⇔\(\left( {\frac{{x + 5}}{{2015}} + 1} \right) + \left( {\frac{{x + 6}}{{2014}} + 1} \right) + \left( {\frac{{x + 7}}{{2013}} + 1} \right) + \left( {\frac{{x + 8}}{{2012}} + 1} \right) + \left( {\frac{{x + 9}}{{2011}} + 1} \right) = 0\)

⇔\(\frac{{x + 2020}}{{2015}} + \frac{{x + 2020}}{{2014}} + \frac{{x + 2020}}{{2013}} + \frac{{x + 2020}}{{2012}} + \frac{{x + 2020}}{{2011}} = 0\)

⇔\(\left( {x + 2020} \right)\left( {\frac{1}{{2015}} + \frac{1}{{2014}} + \frac{1}{{2013}} + \frac{1}{{2012}} + \frac{1}{{2011}}} \right) = 0\)

⇔ x + 2020 = 0

⇔ x = -2020

Vậy x = -2020