Exercice

Décomposer en éléments simples les fractions suivantes :
a) \(I = \) \(\frac{{{x^2} + 2}}{{{{\left( {x + 1} \right)}^3}\left( {x - 2} \right)}}\);
b) \(I = \frac{{{x^4}}}{{{x^2} - 1}}\);
c) \(I = \) \(\frac{{{x^2} + 2}}{{{{\left( {x + 2} \right)}^3}\left( {x - 2} \right)}}\);
d) \(I = \) \(\frac{{{x^2} - 6}}{{{x^4} - 6{x^2} + 8}}\);
e) \(I = \frac{{{x^5}}}{{{x^3} - 1}}\);
f) \(I = \) \(\frac{{2{x^2} - 3x - 3}}{{\left( {x - 1} \right)\left( {{x^2} - 2x + 5} \right)}}\).