<s>[INST] Subtracting $\frac{(x+3)}{(x^2-1)} - \frac{(x-2)}{(x^2+2x+1)}$ $\frac{(x+3)}{(x^2-1)} - \frac{(x-2)}{(x^2+2x+1)}$
To solve the problem I first dissembled the equation on the denominator
 $ \frac{(x+3)}{(x-1)*(x+1)} - \frac{(x-2)}{(x+1)^2}$
I multiplied the denominator together and to do this, I think I have to multiply the top part as well right? This is where i get confused, I forgot how to do this problem as its been a long time. How would i go on to solve this? 
 [/INST] The common factor can be taken to front as coefficient in the numerator as well as in the denominator.
$$ \frac{x+3}{(x-1)(x+1)} - \frac{x-2}{(x+1)^2}=\frac{1}{(x+1)} \cdot [\frac{x+3}{(x-1)} - \frac{x-2}{(x+1)}] $$
$$=\frac{1}{(x+1)} \cdot \frac{(x^2+4 x+ 3) - (x^2- 3 x + 2)}  {(x^2-1)} $$
$$=\frac{1}{(x+1)}  \frac{(7 x + 1)}  {(x^2-1)}. $$
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