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\begin{align}
(-1) + (-1)^2 &= -1 + 1 = 0\\
(-1)-(-1)^2 &= (-1) - 1 = -2
\end{align}
Therefore:
\begin{align}
[(-1) + (-1)^2 ]\div [(-1)-(-1)^2] = 0 \div (-2) = 0
\end{align}

This problem is taken from the UKMT Mathematical Challenges.

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