Thực hiện phép tính: i) ( 2/( x + 2) + 2/( x − 1) ) ⋅ (x^ 2 − 4)/( 4 x ^2 − 1) .

i) \(\left( {\frac{2}{{x + 2}} + \frac{2}{{x - 1}}} \right) \cdot \frac{{{x^2} - 4}}{{4{x^2} - 1}}\)

\( = \frac{{2x - 2 + 2x + 4}}{{\left( {x + 2} \right)\left( {x - 1} \right)}} \cdot \frac{{\left( {x - 2} \right)\left( {x + 2} \right)}}{{\left( {2x - 1} \right)\left( {2x + 1} \right)}}\)

\( = \frac{{4x + 2}}{{x - 1}} \cdot \frac{{x - 2}}{{\left( {2x - 1} \right)\left( {2x + 1} \right)}}\)

\( = \frac{{2\left( {2x + 1} \right)}}{{x - 1}} \cdot \frac{{x - 2}}{{\left( {2x - 1} \right)\left( {2x + 1} \right)}}\)

\( = \frac{{2\left( {x - 2} \right)}}{{\left( {x - 1} \right)\left( {2x - 1} \right)}}.\)