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I'm Nina. I have a really tough homework that counts as a test and I couldn't do it. It's really urgent. Help please!

  1. Let $\alpha \in \Bbb{R}^+$. Let $F$ be the function defined in $\Bbb{R}$ by $$F(x) = \frac{1}{\cosh\alpha - \cos x}.$$ What is the decomposition into simple elements of the fraction? $$ -\frac{2X}{X^2 - (e^{\alpha}+ e^{-\alpha} )X+1} $$

  2. Give an other expression for $\displaystyle -\frac{e^{\alpha}}{e^{ix} - e^{\alpha}}$.

  3. And for $\displaystyle -\frac{e^{\alpha}}{e^{ix} - e^{-\alpha}}$.

And big thanks.

1 Answers 1