Find the Domain (x^2+4x-21)/(x^2+14x+49)

Problem

(x2+4*x−21)/(x2+14*x+49)

Solution

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

2. Set the denominator expression equal to zero to find the excluded values of x

x2+14*x+49=0

3. Factor the quadratic expression in the denominator, recognizing it as a perfect square trinomial.

(x+7)2=0

4. Solve for x by taking the square root of both sides and isolating the variable.

x+7=0

x=−7

5. State the domain as all real numbers except for the value that makes the denominator zero.

Final Answer

Domain: *{x|x∈ℝ,x≠−7}

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