Find the Domain (x^2+12)/(x^2+2x-3)

Problem

(x2+12)/(x2+2*x−3)

Solution

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

x2+2*x−3≠0

2. Factor the quadratic expression in the denominator by finding two numbers that multiply to −3 and add to 2

(x+3)*(x−1)≠0

3. Solve for the excluded values of x by setting each factor to zero.

x+3=0⇒x=−3

x−1=0⇒x=1

4. State the domain as all real numbers except for the values that make the denominator zero.

Domain={x|x∈ℝ,x≠−3,x≠1}

Final Answer

Domain=(−∞,−3)∪(−3,1)∪(1,∞)

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