Question 343996
{{{x^3+4x^2+4x=x(x^2+4x+4)=x(x+2)^2
.
.
.
{{{(3x^2+13x+20)/(x(x+2)^2)=A/x+B/(x+2)+C/(x+2)^2}}}
{{{3x^2+13x+20=A(x+2)^2+Bx(x+2)+Cx}}}
{{{3x^2+13x+20=A(x^2+4x+4)+B(x^2+2x)+Cx}}}
1.{{{x^(2)}}}:{{{A+B=3}}}
2.{{{x^(1)}}}:{{{4A+2B+C=13}}}
3.{{{x^(0)}}}:{{{4A=20}}}
From eq. 3,
{{{A=5}}}
From eq. 1,
{{{5+B=3}}}
{{{B=-2}}}
From eq. 2,
{{{4(5)+2(-2)+C=13}}}
{{{20-4+C=13}}}
{{{C=-3}}}
.
.
.
{{{highlight((3x^2+13x+20)/(x(x+2)^2)=5/x-2/(x+2)-3/(x+2)^2)}}}