Question 952701
{{{(5x^2+20x+6)/(x^2(x-2))=A/x+B/x^2+C/(x-2)}}}
{{{5x^2+20x+6=Ax(x-2)+B(x-2)+Cx^2}}}
{{{5x^2+20x+6=Ax^2-2Ax+Bx-2B+Cx^2}}}
{{{5x^2+20x+6=(A+C)x^2+(B-2A)x-2B}}}
So then,
{{{-2B=6}}}
{{{B=-3}}}
then,
{{{B-2A=20}}}
{{{-3-2A=20}}}
{{{-2A=23}}}
{{{A=-23/2}}}
and
{{{A+C=5}}}
{{{-23/2+C=5}}}
{{{C=5+23/2}}}
{{{C=10/2+23/2}}}
{{{C=33/2}}}
So then,
{{{highlight((5x^2+20x+6)/(x^2(x-2))=-23/(2x)-3/x^2+33/(2(x-2)))}}}