Question

So sánh các số hữu tỉ:

a, x=\(\dfrac{-24}{35}\) ; y=\(\dfrac{-19}{30}\)

b, A= \(\dfrac{2006}{2007}\) - \(\dfrac{2007}{2008}\) + \(\dfrac{2008}{2009}\) - \(\dfrac{2009}{2010}\)

B= \(\dfrac{-1}{2006.2007}\) - \(\dfrac{1}{2008.2009}\)

Answer 1

a) Ta có:

\(-\dfrac{24}{35}< -\dfrac{24}{30}< -\dfrac{19}{30}\)

\(\Rightarrow x< y\)

b) Ta có:

\(A=\dfrac{2006}{2007}-\dfrac{2007}{2008}+\dfrac{2008}{2009}-\dfrac{2009}{2010}\)

\(A=\left(1-\dfrac{1}{2007}\right)-\left(1-\dfrac{1}{2008}\right)+\left(1-\dfrac{1}{2009}\right)-\left(1-\dfrac{1}{2010}\right)\)

\(A=1-\dfrac{1}{2007}-1+\dfrac{1}{2008}+1-\dfrac{1}{2009}-1+\dfrac{1}{2010}\)

\(A=-\dfrac{1}{2007}+\dfrac{1}{2008}-\dfrac{1}{2009}+\dfrac{1}{2010}\)

Ta lại có:

\(B=-\dfrac{1}{2006.2007}-\dfrac{1}{2008.2009}\)

\(B=-\dfrac{1}{2006}+\dfrac{1}{2007}-\dfrac{1}{2008}+\dfrac{1}{2009}\)

=> Dễ dàng thấy A > B