Find the Domain (x-5)/(4x+8)*(12x^2+32x+16)

Problem

(x−5)/(4*x+8)⋅(12*x2+32*x+16)

Solution

1. Identify the expression as a product of a rational function and a polynomial.

2. Determine the restriction for the domain by identifying where the denominator of the rational expression is equal to zero.

3. Set the denominator equal to zero and solve for x

4*x+8=0

4. Subtract 8 from both sides:

4*x=−8

5. Divide by 4 to find the excluded value:

x=−2

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

Final Answer

Domain: *{x|x∈ℝ,x≠−2}

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