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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}

(-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.**View the archive of all weekly problems grouped by curriculum topic*