2000 AMC 12 Problem 11

Combining over a common denominator, $$\frac{a}{b} + \frac{b}{a} - ab = \frac{a^2 + b^2 - (ab)^2}{ab}.$$ Replacing $ab$ with $a - b$ in the numerator, $$\begin{gathered} a^2 + b^2 - (a - b)^2 \\ = a^2 + b^2 \\ {}- (a^2 - 2ab + b^2) \\ = 2ab. \end{gathered}$$ Therefore the expression equals $\dfrac{2ab}{ab} = 2.$ Thus, the correct answer is E.