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

Problem

x/(x2−4)

Solution

1. Identify the condition for the domain of a rational function. A rational function is defined for all real numbers except where the denominator is equal to zero.

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

x2−4=0

3. Solve the quadratic equation by factoring the difference of squares.

(x−2)*(x+2)=0

4. Determine the roots by setting each factor to zero.

x−2=0⇒x=2

x+2=0⇒x=−2

5. State the domain as all real numbers except for the values that make the denominator zero. In interval notation, this excludes −2 and 2

Final Answer

Domain: *(−∞,−2)∪(−2,2)∪(2,∞)

Want more problems? Check here!