Let $$P(x) = \frac{x}{(x+3)(x+2)} = \frac{3}{x+3} - \frac{2}{x+2}$$
I can verify it's true, but I'm not sure how they came up with exactly this polynomal splitting.
Can you please help?
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3Are you familiar with partial fractions? – HDE 226868 Nov 14 '15 at 14:33
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@HDE226868 Probably not :) That's why I've asked this question. That seemed very basic, and that's why I found no solutions for this in my textbooks. – iTayb Nov 14 '15 at 14:41
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Okay; you've got a good answer so far from Aniket to make up for the textbooks, then. – HDE 226868 Nov 14 '15 at 14:44
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Hint: $$\frac{x}{(x+3)(x+2)} = \frac{A}{x+3} + \frac{B}{x+2}$$
i.e. $$x=A(x+2)+B(x+3)$$ which is an identity in $x$.
Now solve for $A$ and $B$ to get the above relation.
SchrodingersCat
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You can even do it faster (if I may suggest) : use $x=-2$ and then $x=-3$ in the equation. Small trick from a lazy old man ! Cheers. – Claude Leibovici Nov 14 '15 at 16:11
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This is a very classical way to do it ! Use it and just get the values without solving (almost) any equation. Cheers :-) – Claude Leibovici Nov 14 '15 at 16:59