6.3 Partial Fractions

Proper

Improper

Both proper and improper

None of the above

Proper

Improper

Both proper and improper

None of the above

Proper

Improper

Both proper and improper

None of the above

 $2+\frac{-3x}{x^2-x-2}$  

 $2+\frac{3x}{x^2-x-2}$  

 $2+\frac{x+8}{x^2-x-2}$  

None, the fraction is proper.

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

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

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

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

 $\frac{A}{(x+3)​}+\frac{B}{(x+3)}​+\frac{C​}{(x-4)}$  

 $\frac{A}{\left(x-4\right)}​+\frac{Bx+C​}{(3+x)^2}$  

 $\frac{A}{(x+3)^2}​+\frac{B}{(x-4)}$  

 $\frac{A}{(x+3)}​+\frac{B}{(x+3)^2}​+\frac{C​}{(x-4)}$  

 $\frac{1}{7}\ and\ \frac{5}{7}$  

 $-\frac{1}{7}\ and\ -\frac{5}{7}$  

 $-\frac{1}{7}\ and\ \frac{5}{7}$  

 $\frac{1}{7}\ and\ -\frac{5}{7}$  

 $2\ and\ 5$  

 $-5\ and\ 2$  

 $2\ and\ -5$  

 $-2\ and\ 5$  

 $\frac{3x}{x+4}-\frac{8x}{x-3}$  

 $\frac{3}{x+4}-\frac{8}{x-3}$  

 $-\frac{21}{x-3}+\frac{16}{x+4}$  

 $-\frac{8}{x+4}+\frac{3}{x-3}$  

 $x-\frac{9}{2}-\frac{5}{2\left(2x-3\right)}+\frac{13}{x+2}$  

 $x-\frac{9}{2}-\frac{5}{2\left(2x-3\right)}-\frac{13}{x+2}$  

 $x+\frac{9}{2}+\frac{5}{2\left(2x-3\right)}+\frac{13}{x+2}$  

 $x-\frac{9}{2}+\frac{5}{2\left(2x-3\right)}+\frac{13}{x+2}$