Question

find all excluded values for the expression.
that is, find all values of t for which the expression is undefined.
\\(\frac{t^2 + 14t + 48}{t^2 + 16t + 64}\\)
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 \( t^2 + 16t + 64 = 0 \).

Step2: Factor the quadratic

Factor the quadratic equation. \( t^2 + 16t + 64 \) is a perfect square trinomial, which factors as \( (t + 8)^2 = 0 \).

Step3: Solve for t

Set each factor equal to zero. Since \( (t + 8)^2 = 0 \), we have \( t + 8 = 0 \), so \( t = -8 \).

Answer:

\( t = -8 \)