Q1)

$\displaystyle \frac{2x+4}{x^2 + 2x - 3} $

From my understanding, I have to always factorize the denominator of the fraction to one of these 3 formulas to proceed on:

1. $\displaystyle \frac{P(x)}{(ax+b)(cx+d)} = \frac{A}{ax+b} + \frac{B}{cx+d}$

2. $\displaystyle \frac{P(x)}{(ax+b)(cx+d)^2} = \frac{A}{ax+b} + \frac{B}{cx+d} + \frac{C}{(cx+d)^2}$

3. $\displaystyle \frac{P(x)}{(ax+b)(cx^2+dx+e)} = \frac{A}{ax+b} + \frac{Bx+C}{cx^2+dx+e} $ where $\displaystyle cx^2+dx+e$ cannot be factored into linear factors (omg i haven't touch on this yet)

However I tried and failed to factorize the denominator to substitute to any of the formulas above.

Please enlighten me! I just need to change them into one of the stated formula and I can to solve it further by myself. Your every effort is appreciated.. Thank you.