Sample quiz on addition/subtraction of rational expressions
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1. What is the common denominator in the expression $\frac{1}{a+b}+\frac{1}{a-b},\quad a\neq b$?
   
   $a^2+b^2$
   $a^2-b^2$
   $a-b$
   $a+b$
   
2. Simplify $\frac{1}{a+b}+\frac{1}{a-b},\quad a\neq b$.
   
   $\frac{2a}{a^2+b^2}$
   $\frac{2b}{a^2-b^2}$
   $\frac{2a}{a^2-b^2}$
   $\frac{2b}{a^2+b^2}$
3. Simplify $\frac{1}{a-b}-\frac{1}{a+b}$.
   
   $\frac{2a}{a^2-b^2}$
   $\frac{2b}{a^2-b^2}$
   $\frac{-2b}{a^2-b^2}$
   $\frac{-2a}{a^2-b^2}$
4. Simplify $\frac{x+1}{x^2+1}-\frac{x}{x+1}$.
   
   $\frac{-x^3+x^2+x+1}{(x^2+1)(x+1)}$
   $\frac{-x^3-x^2+x+1}{(x^2+1)(x+1)}$
   $\frac{x^3+x^2+x+1}{(x^2+1)(x+1)}$
   $\frac{-x^3+x^2+x+1}{(x^2+1)(x+1)}$
5. Simplify $\frac{1}{x^2-1}+\frac{x}{x^2-x-2}$.
   
   $\frac{x^2+2x-2}{(x+1)(x-1)(x-2)}$
   $\frac{x^2-2}{(x+1)(x-1)(x+2)}$
   $\frac{x^2-2x-2}{(x+1)(x-1)(x-2)}$
   $\frac{x^2-2}{(x+1)(x-1)(x-2)}$
6. Simplify $\frac{2x+1}{3x^2+10x+3}-\frac{1}{6x+2}$.
   
   $\frac{3x-1}{2(x+3)(3x-1)}$
   $\frac{3x-1}{2(x+3)(3x+1)}$
   $\frac{3x+1}{2(x-3)(3x+1)}$
   $\frac{1}{2(x+3)}$
7. Simplify $\frac{1}{a}+\frac{1}{b}$.
   
   $\frac{2}{a+b}$
   $\frac{2}{ab}$
   $\frac{ab}{a+b}$
   $\frac{a+b}{ab}$
8. Simplify $\frac{1}{4x^2+4x+1}-\frac{1}{4x^2-4x+1}$.
   
   $\frac{-8x}{(4x^2+1)^2}$
   $\frac{-8x}{(4x^2-1)^2}$
   $\frac{8x}{(4x^2-1)^2}$
   $\frac{8x^2+2}{(4x^2-1)^2}$
9. Assuming $a\neq -1$, simplify $\frac{a^2-9a-10}{a+1}+\frac{a-1}{2a+2}$.
   
   $\frac{3(a+7)}{2}$
   $\frac{3(7-a)}{2}$
   $\frac{3(a^2-7)}{2}$
   $\frac{3(a-7)}{2}$
10. Simplify $\frac{x-1}{x+1}+\frac{x+1}{x-1}$.
    
    $\frac{2x^2+2}{x^2-1}$
    $\frac{2x^2+2}{x^2+1}$
    $\frac{2x^2-2}{x^2-1}$
    $\frac{2x^2+1}{x^2-1}$