Find the Domain

Problem

(x2+x−56)/(x2+x−72)⋅(x2+14*x+48)/(x2−3*x−28)

Solution

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

2. Factor the first denominator x2+x−72 We look for two numbers that multiply to −72 and add to 1 These numbers are 9 and −8

x2+x−72=(x+9)*(x−8)

3. Factor the second denominator x2−3*x−28 We look for two numbers that multiply to −28 and add to −3 These numbers are −7 and 4

x2−3*x−28=(x−7)*(x+4)

4. Set each factor in the denominators to zero to find the excluded values.

(x+9)*(x−8)=0⇒x=−9,x=8

(x−7)*(x+4)=0⇒x=7,x=−4

5. State the domain by excluding these values from the set of all real numbers.

Final Answer

Domain={x|x∈ℝ,x≠−9,−4,7,8}

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