Question

Cho: a = \(\frac{2008}{2009}\) ; b = \(\frac{2009}{2008}\) ; c = \(\frac{1}{2009}\) ; d = \(\frac{2007}{2008}\)

Tìm : a - b+c+d

Answer 1

Có :\(a-b=\frac{2008}{2009}-\frac{2009}{2008}\)\(=\frac{2008^2-2009^2}{2008\cdot2009}=\frac{\left(2008-2009\right)\left(2008+2009\right)}{2008\cdot2009}\)

\(=\frac{-2008-2009}{2008\cdot2009}=-\frac{1}{2009}-\frac{1}{2008}\)

=>a-b+c+d=\(-\frac{1}{2009}-\frac{1}{2008}+\frac{1}{2009}+\frac{2007}{2008}\)

\(=-\frac{1}{2008}+\frac{2007}{2008}=\frac{2006}{2008}=\frac{1003}{1004}\)