Sample quiz on solving rational equations
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1. Solve the equation $\frac{1}{x}=\frac{1}{2}$
   
   $x=1$
   $x=2$
   $x=\frac{1}{2}$
   $x=\sqrt{2}$
   
2. Solve the rational equation $\frac{1}{x+1}=\frac{1}{1-x}$.
   
   $x=0$
   $x=1$
   $x=2$
   $x=-1$
3. Solve the rational equation $\frac{2}{x}=\frac{x}{2}$
   
   $x=2$
   $x=\pm 2$
   $x=\pm 1$
   $x=-2$
4. Solve the equation $\frac{1}{x+1}=2$
   
   $x=-\frac{1}{2}$
   $x=-2$
   $x=\frac{1}{2}$
   $x=\frac{1}{3}$
5. Solve the equation $\frac{3x}{x+1}=1$
   
   $x=\frac{1}{3}$
   $x=\frac{1}{2}$
   $x=-\frac{1}{2}$
   $x=-\frac{1}{3}$
6. Solve the rational equation $\frac{1}{x^2-x+3}=\frac{1}{5}$
   
   $x=-2,1$
   $x=-1,2$
   $x=-1$
   $x=-2$
7. Solve the rational equation $\frac{1}{x}+\frac{1}{x-1}=\frac{3}{2}$
   
   $x=2$
   $x=\frac{1}{3}$
   $x=\frac{1}{2}$
   $x=2,\frac{1}{3}$
8. Solve the rational equation $\frac{1}{x}-\frac{1}{x-1}=-\frac{1}{12}$
   
   $x=-4,3$
   $x=-3,4$
   $x=-3$
   $x=-4$
9. Solve the rational equation $\frac{x^2+x+4}{x^2+x-1}=2$
   
   $x=-3$
   $x=-2$
   $x=-2,3$
   $x=-3,2$
10. Solve the rational equation $\frac{1}{x}=\frac{1}{x+1}$
    
    $x=0$
    $x=1$
    $x=2$
    No solution.