Find the Domain (x+3)/(x-4)*(x^2-2x-8)/(x^2-9)

Problem

(x+3)/(x−4)⋅(x2−2*x−8)/(x2−9)

Solution

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

2. Set each denominator in the product to zero to find the excluded values of x

x−4=0

x2−9=0

3. Solve the first equation for x

x=4

4. Solve the second equation by factoring the difference of squares.

(x−3)*(x+3)=0

x=3

x=−3

5. Combine all excluded values to define the domain as all real numbers except these specific values.

x≠4,3,−3

Final Answer

Domain:{[x∈ℝ,x≠4,x≠3,x≠−3]}

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