Tính đạo hàm của hàm số \(y = \frac{{{x^2} + 2x - 3}}{{x + 2}}\). 

\(y' = \frac{{{{\left( {{x^2} + 2x - 3} \right)}^\prime }.\left( {x + 2} \right) - \left( {{x^2} + 2x - 3} \right).{{\left( {x + 2} \right)}^\prime }}}{{{{\left( {x + 2} \right)}^2}}}\)\( = \frac{{\left( {2x + 2} \right).\left( {x + 2} \right) - \left( {{x^2} + 2x - 3} \right)}}{{{{\left( {x + 2} \right)}^2}}}\)

\( = \frac{{{x^2} + 4x + 7}}{{{{\left( {x + 2} \right)}^2}}}\)\( = \frac{{{x^2} + 4x + 4 + 3}}{{{{\left( {x + 2} \right)}^2}}}\)\( = 1 + \frac{3}{{{{\left( {x + 2} \right)}^2}}}\).