$\frac{A}{\left(x+1\right)}+\frac{B}{\left(3+x\right)}+\frac{C}{\left(3+x\right)^2}$  

 $\frac{A}{\left(x+1\right)}+\frac{Bx+C}{\left(3+x^2\right)}$  

 $\frac{A}{\left(x+1\right)}+\frac{B}{\left(3+x^2\right)}$  

 $\frac{A}{\left(3+x^2\right)}+\frac{Bx}{\left(1+x\right)}$  

proper

improper

both proper and improper

none of the above

 $\frac{3}{x+3}+\frac{3}{x-3}$  

 $\frac{3}{x+3}-\frac{3}{x+3}$  

 $\frac{3}{x-3}+\frac{3}{x-3}$  

 $-\frac{3}{x-3}-\frac{3}{x+3}$  

Linear Factor Method

Repeated Linear Factor Method

Quadratic Factor Method

Log Division Factor Method

proper

improper

both proper and improper

none of the above

 $\frac{A}{\left(x+1\right)}+\frac{B}{\left(3+x\right)}+\frac{C}{\left(3+x\right)^2}$  

 $\frac{A}{\left(x+1\right)}+\frac{Bx+C}{\left(3+x^2\right)}$  

 $\frac{A}{\left(x+1\right)}+\frac{B}{\left(3+x^2\right)}$  

 $\frac{A}{\left(3+x^2\right)}+\frac{Bx}{\left(1+x\right)}$