Find the Domain (x^2-36)/(x^2-3x-18)

Problem

(x2−36)/(x2−3*x−18)

Solution

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

Denominator≠0

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

x2−3*x−18=0

3. Factor the quadratic equation by finding two numbers that multiply to −18 and add to −3

(x−6)*(x+3)=0

4. Solve for x by setting each factor to zero using the zero product property.

x−6=0⇒x=6

x+3=0⇒x=−3

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

x≠6,x≠−3

Final Answer

Domain: *(−∞,−3)∪(−3,6)∪(6,∞)

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