<s>[INST] Decompose a fraction in a sum of two Let's say that I have this fraction:
$$ \frac{2x}{x^2+4x+3}$$
I would like to decompose in two fraction:
$$ \frac{A}{x+3} + \frac{B}{x+1}$$
Which is the procedure for that?  :)
 [/INST] Hint:
$$\frac{A}{x+3} + \frac{B}{x+1} = \frac{A(x+1) + B(x+3)}{(x+1)(x+3)} = \frac{(A+B)x + (A+3B)}{x^2+4x+3} = \frac{2x}{x^2+4x+3}$$
What must the values of $A$ and $B$ so that $A+B = 2$ and $A + 3B = 0$?
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