Find the Domain (t^2-6t-27)/(t^2-36)

Problem

(t2−6*t−27)/(t2−36)

Solution

1. Identify the condition for the domain of a rational function, which requires that the denominator cannot be equal to zero.

t2−36≠0

2. Factor the denominator using the difference of squares formula, a2−b2=(a−b)*(a+b)

(t−6)*(t+6)≠0

3. Solve for the excluded values by setting each factor to zero.

t−6=0⇒t=6

t+6=0⇒t=−6

4. State the domain by excluding these values from the set of all real numbers.

Domain={[t∈ℝ,t≠6,t≠−6]}

Final Answer

Domain=(−∞,−6)∪(−6,6)∪(6,∞)

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