Find the Domain (x^2+x+7)/(x^2-225)

Problem

(x^2+x+7)/(x^2−225)

Solution

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

x^2−225≠0

2. Set the denominator equal to zero to find the excluded values of x

x^2−225=0

3. Factor the expression using the difference of squares formula, a^2−b^2=(a−b)*(a+b)

(x−15)*(x+15)=0

4. Solve for x by setting each factor to zero.

x−15=0⇒x=15

x+15=0⇒x=−15

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

Domain={x|x∈ℝ,x≠15,x≠−15}

Final Answer

Domain=(−∞,−15)∪(−15,15)∪(15,∞)

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