Find the Domain (3x)/(x^2-4)

Problem

Domain of (3*x)/(x2−4)

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

x2−4=0

3. Factor the difference of squares on the left side of the equation.

(x−2)*(x+2)=0

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

x−2=0⇒x=2

x+2=0⇒x=−2

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

x≠2,x≠−2

Final Answer

Domain: *(−∞,−2)∪(−2,2)∪(2,∞)

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