Find the Domain (v^2-8v+15)/(45-5v^2)

Problem

(v2−8*v+15)/(45−5*v2)

Solution

1. Identify the condition for the domain of a rational function, which requires that the denominator is not equal to zero.

45−5*v2≠0

2. Factor the denominator by first pulling out the greatest common factor.

5*(9−v2)≠0

3. Apply the difference of squares formula to factor the expression inside the parentheses.

5*(3−v)*(3+v)≠0

4. Solve for the values of v that make the denominator zero by setting each factor to zero.

3−v=0⇒v=3

3+v=0⇒v=−3

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

v≠3,v≠−3

Final Answer

Domain: *{v|v∈ℝ,v≠3,v≠−3}

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