Find the Domain (5x-8)/(x^2-25)

Problem

(5*x−8)/(x2−25)

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 expression equal to zero to find the excluded values of x

x2−25=0

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

(x−5)*(x+5)=0

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

x−5=0⇒x=5

x+5=0⇒x=−5

5. State the domain as all real numbers except for the values that make the denominator zero.

Final Answer

Domain: *{x|x∈ℝ,x≠5,x≠−5}

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