$\frac{1000^2}{252^2-248^2}$ equals
$\mathrm{(A) \  }62,500 \qquad \mathrm{(B) \  }1,000 \qquad \mathrm{(C) \  } 500\qquad \mathrm{(D) \  }250 \qquad \mathrm{(E) \  } \frac{1}{2}$
We can use [difference of squares](https://artofproblemsolving.com/wiki/index.php/Difference_of_squares) to factor the [denominator](https://artofproblemsolving.com/wiki/index.php/Denominator), yielding:
$\frac{1000^2}{252^2-248^2}=\frac{1000^2}{(252-248)(252+248)}=\frac{1000^2}{(4)(500)}=\frac{1000^2}{2000}$.
We see that the $1000$ in the denominator cancels with one of the $1000$s in the [numerator](https://artofproblemsolving.com/wiki/index.php/Numerator), yielding $500, \boxed{\text{C}}$.