Thực hiện phép tính:  a) x/(x + 9) + 9/(x + 9) b) x/(x + 6)- 36/(x^2) + 6x)

Hướng dẫn giải

a) \(\frac{x}{{x + 9}} + \frac{9}{{x + 9}}\)\( = \frac{{x + 9}}{{x + 9}} = 1.\)

b) \(\frac{x}{{x + 6}} - \frac{{36}}{{{x^2} + 6x}} = \frac{{{x^2} - 36}}{{x\left( {x + 6} \right)}} = \frac{{\left( {x + 3} \right)\left( {x - 3} \right)}}{{x\left( {x + 6} \right)}}\)\( = \frac{{x - 6}}{x}.\)

c) \[\frac{{7x + 1}}{{x - 3}} \cdot \frac{{x - 5}}{{x + 7}} - \frac{{x - 5}}{{x + 7}} \cdot \frac{{6x - 6}}{{x - 3}} = \frac{{x - 5}}{{x + 7}} \cdot \left( {\frac{{7x + 1}}{{x - 3}} - \frac{{6x - 6}}{{x - 3}}} \right)\]

\[ = \frac{{x - 5}}{{x + 7}} \cdot \frac{{7x + 1 - 6x + 6}}{{x - 3}}\]\( = \frac{{x - 5}}{{x - 3}}.\)