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

Problem

h(x)=(2*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.

x2−1≠0

2. Factor the quadratic expression in the denominator using the difference of squares formula.

(x−1)*(x+1)≠0

3. Solve for the values of x that make the denominator zero by setting each factor to zero.

x−1=0⇒x=1

x+1=0⇒x=−1

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

x≠1,x≠−1

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

(−∞,−1)∪(−1,1)∪(1,∞)

Final Answer

Domain:(−∞,−1)∪(−1,1)∪(1,∞)

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