Find the Domain (n-10)/(4n^2)*(n^2-36)/(n^2-4n-60)

Problem

(n−10)/(4*n2)⋅(n2−36)/(n2−4*n−60)

Solution

1. Identify the expression as a product of two rational functions.

2. Determine the conditions for the domain by identifying all values of n that would make any denominator in the expression equal to zero.

3. Set the first denominator to zero and solve for n

4*n2=0

n=0

4. Set the second denominator to zero and solve for n by factoring the quadratic expression:

n2−4*n−60=0

(n−10)*(n+6)=0

n=10

n=−6

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

Final Answer

Domain={[n∈ℝ,n≠−6,0,10]}

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