Find the Domain (y^2-6y-16)/(y^2+10y+21)

Problem

(y2−6*y−16)/(y2+10*y+21)

Solution

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

y2+10*y+21≠0

2. Factor the quadratic expression in the denominator by finding two numbers that multiply to 21 and add to 10

(y+3)*(y+7)≠0

3. Solve for the values of y that make the denominator zero by setting each factor to zero.

y+3=0⇒y=−3

y+7=0⇒y=−7

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

y≠−3,y≠−7

Final Answer

Domain: *{[y∈ℝ,y≠−3,y≠−7]}

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