Rút gọn các biểu thức sau: a) (2x - 7)/(5x - 12) + (3x - 5)/(5x - 12). b)(2x - 1)/(x + 1) - ((x^2)- x + 1)/((x^2) + x).(x^2)/(x - 1)

Hướng dẫn giải

a) \[\frac{{2x - 7}}{{5x - 12}} + \frac{{3x - 5}}{{5x - 12}}\]\[ = \frac{{2x - 7 + 3x - 5}}{{5x - 12}} = \frac{{5x - 12}}{{5x - 12}} = 1.\]

b) \[\left( {\frac{{2x - 1}}{{x + 1}} - \frac{{{x^2} - x + 1}}{{{x^2} + x}}} \right) \cdot \frac{{{x^2}}}{{x - 1}}\]\[ = \left[ {\frac{{2x - 1}}{{x + 1}} - \frac{{{x^2} - x + 1}}{{x\left( {x + 1} \right)}}} \right] \cdot \frac{{{x^2}}}{{x - 1}}.\]

\[ = \left[ {\frac{{2{x^2} - x}}{{x\left( {x + 1} \right)}} - \frac{{{x^2} - x + 1}}{{x\left( {x + 1} \right)}}} \right] \cdot \frac{{{x^2}}}{{x - 1}}\]\[ = \frac{{{x^2} - 1}}{{x\left( {x + 1} \right)}} \cdot \frac{{{x^2}}}{{x - 1}}\]\[ = x.\]