Question 950724
Dividing first,
{{{(3x^3-x^2-13x-13) / (x^2-x-6)=(3x+2)+(7x-1)/(x^2-x-6)}}}
So then,
{{{(7x-1)/((x-3)(x+2))=A/(x-3)+B/(x+2)}}}
{{{7x-1=A(x+2)+B(x-3)}}}
{{{7x-1=(A+B)x+(2A-3B)}}}
which leads to,
{{{A+B=7}}}
{{{2A-3B=-1}}}
Multiply the first by 2 and subtract from the second to eliminate {{{A}}},
{{{2A-3B-2A-2B=-1-14}}}
{{{-5B=-15}}}
{{{B=3}}}
Then,
{{{A+3=7}}}
{{{A=4}}}
So finally,
{{{(3x^3-x^2-13x-13) / (x^2-x-6)=(3x+2)+4/(x-3)+3/(x+2)}}}