Решение:
\[ \frac{t^2-100}{t^2+20t+100} = \frac{(t-10)(t+10)}{(t+10)^2} = \frac{t-10}{t+10} \]
\[ \frac{t-10}{t+10} = \frac{-8-10}{-8+10} = \frac{-18}{2} = -9 \]
Ответ: -9