Thực hiện phép tính: a) 4x + 13/ 5x ( x-7 ) + x -48 / 5x ( x-7)

a) \[\frac{{4x + 13}}{{5x\left( {x - 7} \right)}} + \frac{{x - 48}}{{5x\left( {x - 7} \right)}} = \frac{{4x + 13 + x - 48}}{{5x\left( {x - 7} \right)}} = \frac{{5x - 35}}{{5x\left( {x - 7} \right)}} = \frac{{5\left( {x - 7} \right)}}{{5x\left( {x - 7} \right)}} = \frac{1}{x}.\]                      

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

\[ = \frac{{{{\left( {x + 2} \right)}^2}}}{{2\left( {x - 2} \right)\left( {x + 2} \right)}} + \frac{{ - 4x \cdot 2}}{{2\left( {x - 2} \right)\left( {x + 2} \right)}} = \frac{{{x^2} + 4x + 4 - 8x}}{{2\left( {x - 2} \right)\left( {x + 2} \right)}} = \frac{{{x^2} - 4x + 4}}{{2\left( {x - 2} \right)\left( {x + 2} \right)}}\]

\[ = \frac{{{{\left( {x - 2} \right)}^2}}}{{2\left( {x - 2} \right)\left( {x + 2} \right)}} = \frac{{x - 2}}{{2\left( {x + 2} \right)}}.\]