1. We are asked to find the limit \( \lim_{t \to 1} \frac{t^2 - 1}{t - 1} \).\n2. Notice that directly substituting \(t = 1\) gives \(\frac{1^2 - 1}{1 - 1} = \frac{0}{0}\), which is an indeterminate form. So, we need to simplify the expression.\n3. Factor the numerator using the difference of squares formula: \(t^2 - 1 = (t - 1)(t + 1)\).\n4. Substitute this back into the limit expression: \n\[ \lim_{t \to 1} \frac{(t - 1)(t + 1)}{t - 1} \]\n5. For \( t \neq 1 \), we can cancel \(t - 1\) terms, so the expression simplifies to \( \lim_{t \to 1} (t + 1) \).\n6. Now, substitute \( t = 1 \) directly: \( 1 + 1 = 2 \).\n7. Therefore, the limit is \(2\).