Partial Fractions - combinatorics - trouble Having a very hard time with this question:
Q:  Use partial fractions to find the power series expansion of $$\frac{1+5x}{1-2x-3x^2}$$

I just want to show how to apply Partial Fraction Decomposition
$$\frac{1+5x}{1-2x-3x^2}=\frac{1+5x}{(1-3x)(1+x)}=\frac A{1-3x}+\frac B{1+x}$$
$$\implies 1+5x=A(1+x)+B(1-3x)=x(A-3B)+A+B$$
Comparing the coefficients of the different powers of $x,A+B=1,A-3B=5$ 
$\implies B=-1,A=2$
Alternatively,
putting $x+1=0\implies x=-1,\quad 1+5\cdot(-1)=A\cdot0+B\cdot\{1-3(-1)\}\implies B=-1 $
putting $1-3x=0\implies x=\frac{1}{3},\quad 1+5\cdot\left(\frac13\right)=A\cdot\left(1+\frac13\right)+B\cdot0\implies A=2 $
