Question

find all excluded values for the expression.
that is, find all values of t for which the expression is undefined.
\\(\frac{t^2 - 2t - 15}{t^2 + 11t + 24}\\)
if there is more than one value, separate them with commas.
\\(t = \square\\)

Explanation:

Step1: Identify undefined condition

A rational expression is undefined when its denominator is zero. So, set the denominator \( t^2 + 11t + 24 = 0 \).

Step2: Factor the quadratic equation

Factor \( t^2 + 11t + 24 \). We need two numbers that multiply to 24 and add to 11. Those numbers are 3 and 8. So, \( t^2 + 11t + 24=(t + 3)(t + 8) \).

Step3: Solve for t

Set each factor equal to zero:

• For \( t + 3 = 0 \), we get \( t=-3 \).
• For \( t + 8 = 0 \), we get \( t=-8 \).

Answer:

\( t = -8, -3 \)