Thực hiện phép tính: 

a) \(\frac{x}{{x + 7}} + \frac{7}{{x + 7}}.\)    

b) \(\frac{x}{{x + 2}} - \frac{4}{{{x^2} + 2x}}.\)      

c) \(\frac{{3x + 1}}{{x - 13}} \cdot \frac{{x - 2}}{{x + 3}} - \frac{{x - 2}}{{x + 3}} \cdot \frac{{2x + 14}}{{x - 13}}.\)

a) \(\frac{x}{{x + 7}} + \frac{7}{{x + 7}}\)\( = \frac{{x + 7}}{{x + 7}} = 1.\)

b) \(\frac{x}{{x + 2}} - \frac{4}{{{x^2} + 2x}} = \frac{{{x^2} - 4}}{{x\left( {x + 2} \right)}} = \frac{{\left( {x + 2} \right)\left( {x - 2} \right)}}{{x\left( {x + 2} \right)}} = \frac{{x - 2}}{x}.\)

c) \[\frac{{3x + 1}}{{x - 13}} \cdot \frac{{x - 2}}{{x + 3}} - \frac{{x - 2}}{{x + 3}} \cdot \frac{{2x + 14}}{{x - 13}} = \frac{{x - 2}}{{x + 3}}\left( {\frac{{3x + 1}}{{x - 13}} - \frac{{2x + 14}}{{x - 13}}} \right)\]

\[ = \frac{{x - 2}}{{x + 3}} \cdot \frac{{3x + 1 - 2x - 14}}{{x - 13}} = \frac{{x - 2}}{{x + 3}} \cdot \frac{{x - 13}}{{x - 13}} = \frac{{x - 2}}{{x + 3}}.\]