Réponse:
[tex] \frac{1}{ {x}^{2} - 4} = \frac{a}{x - 2} + \frac{b}{x + 2} [/tex]
[tex] \frac{1}{ {x}^{2} - 4} = \frac{a(x + 2)}{(x - 2)(x + 2)} + \frac{b(x - 2) }{(x - 2)(x + 2)}[/tex]
[tex] \frac{1}{ {x}^{2} - 4 } = \frac{a(x + 2) + b(x - 2)}{(x - 2)(x + 2)} [/tex]
[tex] \frac{1}{ {x}^{2} - 4 } = \frac{a(x + 2) + b(x - 2)}{ {x}^{2} - {2}^{2} } [/tex]
[tex]1 = a(x + 2) + b(x - 2)[/tex]
[tex]a = \frac{1}{2} \: \: \: \: \: \: \: \: b = - \frac{1}{2} [/tex]
