Find the Domain (3r-9)/(4r^2+8r)*(2r+4)/(18-6r)

Problem

(3*r−9)/(4*r2+8*r)⋅(2*r+4)/(18−6*r)

Solution

1. Identify the condition for the domain of a rational expression, which requires that the denominators of all terms in the expression must not equal zero.

2. Set the first denominator to zero and solve for r

4*r2+8*r=0

4*r*(r+2)=0

r≠0

r≠−2

3. Set the second denominator to zero and solve for r

18−6*r=0

18=6*r

r≠3

4. Combine all restrictions to define the domain as all real numbers except those that make any denominator zero.

Final Answer

Domain:{r|r∈ℝ,r≠0,r≠−2,r≠3}

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