problem: What fraction is the same as \[
  \frac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21}?
  \]
solution: We have \begin{align*}
  &\frac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21} \\
  & \qquad = \frac{2(1-2+3-4+5-6+7)}{3(1-2+3-4+5-6+7)} \\
  & \qquad = \boxed{\frac{2}{3}}.
  \end{align*}