Cho phương trình:
a) \(\frac{x+2}{2002}\)+\(\frac{x+5}{1999}\)+\(\frac{x+201}{1803}\)=-3
b) \(\frac{x+5}{2015}\)+\(\frac{x+3}{2017}\)= \(\frac{x+4}{2016}\)+\(\frac{x+2}{2018}\)
c) \(\frac{x+1}{65}\)+\(\frac{x+3}{63}\)=\(\frac{x+5}{65}\)+\(\frac{x+7}{59}\)
d) \(\frac{x-1}{x}\)+\(\frac{1}{x+1}\)=\(\frac{2x-1}{x^2+x}\)
a) \(\frac{x+2}{2002}\)+\(\frac{x+5}{1999}\)+\(\frac{x+201}{1803}\)=-3
⇔\(\frac{x+2}{2002}\)+\(\frac{x+5}{1999}\)+\(\frac{x+201}{1803}\)+3=0
⇔\(\frac{x+2}{2002}\)+1+\(\frac{x+5}{1999}\)+1+\(\frac{x+201}{1803}\)+1=0
⇔\(\frac{x+2004}{2002}\)+\(\frac{x+2004}{1999}\)+\(\frac{x+2004}{1803}\)=0
⇔(x+2004)(\(\frac{1}{2002}\)+\(\frac{1}{1999}\)+\(\frac{1}{1803}\))=0
Mà (\(\frac{1}{2002}\)+\(\frac{1}{1999}\)+\(\frac{1}{1803}\))≠0
⇒x+2004=0
⇔x=-2004
Vậy tập nghiệm của phương trình đã cho là:S={-2004}
