Find the Domain (n^(2-15n+56))/(n^(2-12n+36))

Problem

(n2−15*n+56)/(n2−12*n+36)

Solution

1. Identify the condition for the domain of a rational function. The domain consists of all real numbers except those that make the denominator equal to zero.

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

n2−12*n+36=0

3. Factor the quadratic expression in the denominator. This is a perfect square trinomial.

(n−6)2=0

4. Solve for n by taking the square root of both sides.

n−6=0

n=6

5. State the domain by excluding the value n=6 from the set of all real numbers.

Final Answer

Domain: *{[n∈ℝ,n≠6]}

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