Find the Domain 3/(x^2-2x-15)

Problem

Domain of 3/(x2−2*x−15)

Solution

1. Identify the condition for the domain of a rational function. The denominator cannot be equal to zero because division by zero is undefined.

Denominator≠0

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

x2−2*x−15=0

3. Factor the quadratic expression by finding two numbers that multiply to −15 and add to −2 These numbers are −5 and 3

(x−5)*(x+3)=0

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

x−5=0⇒x=5

x+3=0⇒x=−3

5. Exclude these values from the set of all real numbers to define the domain.

x≠5,x≠−3

Final Answer

Domain: *(−∞,−3)∪(−3,5)∪(5,∞)

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