Find the Domain (x^2-25)/(x^2-9)

Problem

(x2−25)/(x2−9)

Solution

1. Identify the condition for the domain of a rational function. The domain consists of all real numbers except those that make the denominator equal to zero.

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

x2−9=0

3. Solve for x by factoring the difference of squares or by taking the square root of both sides.

x2=9

x=±3

4. State the domain by excluding these values from the set of all real numbers. In interval notation, this represents all numbers except −3 and 3

Final Answer

Domain:(−∞,−3)∪(−3,3)∪(3,∞)

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