Sample quiz on multiplication/division of rational expressions
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1. Assuming appropriate restrictions, simplify $\frac{x+1}{x-1}\times\frac{1}{2x^2-2}$.
   
   $\frac{1}{2(x+1)^2}$
   $\frac{1}{(x-1)^2}$
   $\frac{1}{2(x-1)^2}$
   $\frac{1}{2(x-2)^2}$
   
2. Assuming appropriate restrictions, simplify the rational expression $\frac{4x-8}{x^2-x-2}$.
   
   $\frac{4}{x+1}$
   $\frac{2}{x+1}$
   $\frac{2}{x-1}$
   $\frac{4}{x-1}$
3. Simplify $\frac{3a^2-12}{a^2+5a+6}$, stating restrictions on $a$.
   
   $\frac{3(a+2)}{a+3},\quad a\neq -2,-3$
   $\frac{3(a-2)}{a+3},\quad a\neq -2,-3$
   $\frac{3(a-2)}{a+3},\quad a\neq -3,2$
   $\frac{3(a-2)}{a+3},\quad a\neq 2,3$
4. Simplify $\frac{y-1}{3y^2+10y+3}\div\frac{5-5y}{2y+6}$.
   
   $\frac{-2}{5(3y-1)}$
   $\frac{-2}{5(3y+1)}$
   $\frac{-2}{5(y+3)}$
   $\frac{-2}{3(3y+1)}$
5. Simplify $\frac{1-x}{x^2+2x+1}\times\frac{2x+2}{4x^2-4}$
   
   $\frac{1}{2(x+1)^2}$
   $\frac{-1}{4(x+1)^2}$
   $\frac{-1}{2(x+1)^2}$
   $\frac{-1}{2(x-1)^2}$
6. Simplify $\frac{a-b}{a^2+ab-2b^2}\div(\frac{1}{a^2+3ab+2b^2})$
   
   $a+b$
   $a+2b$
   $\frac{1}{a+b}$
   $\frac{a-b}{a+b}$
7. Simplify $\frac{a^2b^3-2ab^2}{5a^2b^2-20}$.
   
   $\frac{a^2b^2}{5(ab+2)}$
   $\frac{ab^2}{5(ab-2)}$
   $\frac{ab^2}{5(ab+2)}$
   $\frac{ab^3}{5(ab+2)}$.
8. Simplify $\frac{1}{a}\div\frac{1}{b}$.
   
   $\frac{a}{b}$
   $\frac{b}{a}$
   $\frac{1}{ab}$
   $\frac{2}{ab}$
9. Simplify $\frac{a^4-a^2b^2}{a^3}\div\frac{a+b}{5a}$.
   
   $\frac{a-b}{5}$
   $\frac{a+b}{5}$
   $5(a-b)$
   $5(a+b)$
10. Simplify $\frac{y^2-3y-10}{3y^2-6y-24}\div\frac{y^2-25}{12}$.
    
    $\frac{4}{(y+4)(y-5)}$
    $\frac{4}{(y+4)(y+5)}$
    $\frac{12}{(y-4)(y+5)}$
    $\frac{4}{(y-4)(y+5)}$