Find the Domain (3x-1)/((x+3)(x-1))

Problem

(3*x−1)/((x+3)*(x−1))

Solution

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

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

(x+3)*(x−1)=0

3. Apply the zero product property to solve for x by setting each factor to zero.

x+3=0⇒x=−3

x−1=0⇒x=1

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

5. Express the domain in interval notation, representing all real numbers except −3 and 1

Final Answer

Domain: *(−∞,−3)∪(−3,1)∪(1,∞)

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