Find the Domain (x^2-25)/(x^2-2x-15)*(x+3)/x

Problem

(x2−25)/(x2−2*x−15)⋅(x+3)/x

Solution

1. Identify the conditions for the domain of a rational expression. The domain consists of all real numbers except those that make any denominator in the expression equal to zero.

2. Set each denominator in the expression equal to zero to find the excluded values.

x2−2*x−15=0

x=0

3. Factor the quadratic denominator to solve for x

(x−5)*(x+3)=0

4. Solve for the roots of the denominators.

x−5=0⇒x=5

x+3=0⇒x=−3

x=0

5. Exclude these values from the set of all real numbers. The domain includes all x such that x≠5 x≠−3 and x≠0

Final Answer

Domain:{[x∈ℝ,x≠−3,0,5]}

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