<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] Add both:
$$\frac{2x}{x^2+4x+3}=\frac{Ax+A+Bx+3B}{x^2+4x+3}$$
$$\frac{2x}{x^2+4x+3}=\frac{(A+B)x+(A+3B)}{x^2+4x+3}$$
Then how this must be valid for all $x$ then $A+B=2$ and $A+3B=0$
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