Question 935920
removed solution because it was wrong;


You really might've mean to include several terms as the numerator, meaning
{{{(6x^3+6x^2 +28x+33)/(x^2+5)^3}}}


The work done on paper was very very lengthy.  One would go with


{{{(Ax+B)/(x^2+5)+(Cx+D)/(x^2+5)^2+(Ex+F)/(x^2+5)^3}}}


Raising to higher terms, comparing corresponding parts after simplification would indicate values:
{{{A=0}}}
{{{B=0}}}
{{{C=6}}}
{{{D=6}}}
{{{E=-2}}}
{{{F=3}}}
And you would want to see that whole process, but like said, very lengthy set of steps on paper, and so very likely to make type-written mistakes on attempt to put the solution process here.


You will be able to substitute the values to show
{{{(6x+6)/(x^2+5)^2+(-2x+3)/(x^2+5)}}}


You lost one partial expression because of the A=0 and B=0.