\[\begin{array}{l}
\frac{2}{{3.5}} + \frac{7}{{5.12}} + \frac{9}{{4.39}} = \frac{1}{5}\left( {\frac{2}{3} + \frac{7}{{12}}} \right) + \frac{9}{{4.39}}\\
= \frac{1}{5}.\frac{5}{4} + \frac{9}{{4.39}} = \frac{1}{4} + \frac{9}{{4.39}} = \frac{1}{4}\left( {1 + \frac{9}{{39}}} \right)\\
= \frac{1}{4}.\frac{{16}}{{13}} = \frac{4}{{13}}.
\end{array}\]
\[\begin{array}{l}
b)\,\,1 - \frac{1}{{1.2}} + 1 - \frac{1}{{2.3}} + ...... + 1 - \frac{1}{{2013.2014}}\\
= 1 - \left( {1 - \frac{1}{2}} \right) + 1 - \left( {\frac{1}{2} - \frac{1}{3}} \right) + ..... + 1 - \left( {\frac{1}{{2013}} - \frac{1}{{2014}}} \right)\\
= 1 - 1 + \frac{1}{2} + 1 - \frac{1}{2} + \frac{1}{3} + ..... + 1 - \frac{1}{{2013}} + \frac{1}{{2014}}\\
= \underbrace {1 + 1 + ... + 1}_{2012\,\,\,chu\,\,so\,\,1} + \frac{1}{{2014}} = 2012 + \frac{1}{{2014}} = \frac{{2012.2014 + 1}}{{2014}}.
\end{array}\]
Câu c bạn làm tương tự.
