Find the Domain (x+4)/(x^2-9)

Problem

(x+4)/(x2−9)

Solution

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

x2−9≠0

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

(x−3)*(x+3)≠0

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

x−3≠0⇒x≠3

x+3≠0⇒x≠−3

4. Express the domain in interval notation, excluding the values −3 and 3

(−∞,−3)∪(−3,3)∪(3,∞)

Final Answer

Domain:(−∞,−3)∪(−3,3)∪(3,∞)

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