Distinct Linear
 $\frac{8}{3\ x-7}+\frac{9}{4\ x+13}$  
 $\frac{\left(A\ x+B\right)+\left(C\ x-D\right)}{\left(3\ x-7\right)\cdot\left(4\ x+13\right)}$  
 $\frac{E\ x+F}{G\ x^{\ 2}+H\ x-K}$  
Submit  $A,B,C,D,E,F,G,H,K$  

(a)  

Distinct Linear
 $\frac{25}{8\ x-3}-\frac{12}{4\ x+5}$  
 $\frac{\left(A\ x+B\right)-\left(C\ x-D\right)}{\left(8\ x-3\right)\cdot\left(4\ x+5\right)}$  
 $\frac{E\ x+F}{G\ x^{\ 2}+H\ x-K}$  
Submit  $A,B,C,D,E,F,G,H,K$  

(a)  

 Repeated Linear
 $\frac{9}{x-12}+\frac{6\ x+19}{\left(x-12\right)^{\ 2}}$  
 $\frac{\left(A\ x-B\right)+\left(C\ x+D\right)}{\left(x-12\right)^{\ 2}}$  
 $\frac{E\ x-F}{x^{\ 2}-H\ x+K}$  
Submit  $A,B,C,D,E,F,H,K$  

(a)  

 Repeated Linear
 $\frac{23}{7\ x-16}-\frac{5\ x-9}{\left(7\ x-16\right)^{\ 2}}$  
 $\frac{\left(A\ x-B\right)-\left(C\ x-D\right)}{\left(7\ x-16\right)^{\ 2}}$  
 $\frac{E\ x-F}{G\ x^{\ 2}-H\ x+K}$  
Submit  $A,B,C,D,E,F,G,H,K$  

(a)  

 Repeated Linear
 $\frac{18}{x}+\frac{11}{x^{\ 2}}+\frac{7}{x^{\ 3}}$  
 $\frac{A\ x^{\ 2}+B\ x+C}{x^{\ D}}$ 
Submit  $A,B,C,D$  

(a)  

 Linear Quadratic (prime)
 $\frac{4}{x-3}+\frac{6\ x+5}{x^{\ 2}+x+1}$  
 $\frac{\left(A\ x^{\ 2}+B\ x+C\right)+\left(D\ x^{\ 2}-E\ x-F\right)}{\left(x-3\right)\cdot\left(x^{\ 2}+x+1\right)}$  
 $\frac{G\ x^2-H\ x-K}{\left(x-3\right)\cdot\left(x^{\ 2}+x+1\right)}$  
Submit  $A,B,C,D,E,F,G,H,K$  

(a)  

 Linear (one common)
 $\frac{4\ x}{x^{\ 2}+9\ x+14}-\frac{2\ x+5}{x^{\ 2}+3\ x-28}$  
 $\frac{\left(A\ x^{\ 2}-B\ x\right)-\left(D\ x^{\ 2}+E\ x+F\right)}{\left(x+7\right)\cdot\left(x+2\right)\cdot\left(x-4\right)}$  
 $\frac{G\ x^2-H\ x-K}{\left(x+7\right)\cdot\left(x+2\right)\cdot\left(x-4\right)}$  
Submit  $A,B,D,E,F,G,H,K$  

(a)  

 Linear (one common)
 $\frac{7\ x}{x^{\ 2}-9\ x-10}+\frac{4}{x^{\ 2}-100}$  
 $\frac{\left(A\ x^{\ 2}+B\ x\right)+\left(E\ x+F\right)}{\left(x+10\right)\cdot\left(x+1\right)\cdot\left(x-10\right)}$  
 $\frac{A\ x^2+G\ x+F}{\left(x+10\right)\cdot\left(x+1\right)\cdot\left(x-10\right)}$  
Submit  $A,B,E,F,G$  

(a)  

 Linear (one common)
 $\frac{3\ x}{x^{\ 2}+4\ x-12}-\frac{2\ x-5}{x^{\ 2}+2\ x-24}$  
 $\frac{\left(A\ x^{\ 2}-B\ x\right)-\left(D\ x^{\ 2}-E\ x+F\right)}{\left(x+6\right)\cdot\left(x-2\right)\cdot\left(x-4\right)}$  
 $\frac{x^2-G\ x-H}{\left(x+6\right)\cdot\left(x-2\right)\cdot\left(x-4\right)}$  
Submit  $A,B,D,E,F,G,H$  

(a)