Find the Domain x/(x^2-1)

Problem

x/(x2−1)

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

x2−1=0

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

(x−1)*(x+1)=0

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

x−1=0⇒x=1

x+1=0⇒x=−1

5. State the domain by excluding these values from the set of all real numbers.

Domain={x|x≠1,x≠−1}

Final Answer

Domain=(−∞,−1)∪(−1,1)∪(1,∞)

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