Thực hiện phép tính: a) 2x(4-3x). b) x/(x - 2) + 3/(x + 2)+ (6 - 7x)/((x^2)- 4)

Hướng dẫn giải

a) \[2x\left( {4-3x} \right)\]

\[ = 8x-6{x^2}.\]

b) \[\frac{x}{{x - 2}} + \frac{3}{{x + 2}} + \frac{{6 - 7x}}{{{x^2} - 4}}\]

\[\frac{x}{{x - 2}} + \frac{3}{{x + 2}} + \frac{{6 - 7x}}{{\left( {x - 2} \right)\left( {x + 2} \right)}}\]

\[ = \frac{{x\left( {x + 2} \right)}}{{x - 2}} + \frac{{3\left( {x - 2} \right)}}{{x + 2}} + \frac{{6 - 7x}}{{\left( {x - 2} \right)\left( {x + 2} \right)}}\]

\[ = \frac{{{x^2} + 2x + 3x - 6 + 6 - 7x}}{{\left( {x - 2} \right)\left( {x + 2} \right)}}\]

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

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