Question 1007683
{{{((7x^2)+45x+58)/((x+3)^2(x+1))=A/(x+3)^2+B/(x+3)+C/(x+1)}}}


RightHandSide,
{{{(A(x+1)+B(x+3)(x+1)+C(x+3)^2)/((x+3)^2*(x+1))}}}


Continue to simplify.  The numerator becomes
{{{(B+C)x^2+(A+4B+6C)x+(A+3B+9C)}}}
Compare then to the numerator in the given expression.


Solve the system  {{{system(B+C=7,A+4B+6C=45,A+3B+9C=58)}}}.


( A quick run through the system of equations gave  A=7,B=2,C=5).