Find the Domain (7x-21)/(5x+15)*(14x+42)/(10x-30)

Problem

(7*x−21)/(5*x+15)⋅(14*x+42)/(10*x−30)

Solution

1. Identify the denominators of the expression, as the domain of a rational function is restricted where the denominator equals zero.

2. Set the first denominator equal to zero and solve for x

5*x+15=0

5*x=−15

x=−3

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

10*x−30=0

10*x=30

x=3

4. Exclude these values from the set of all real numbers to define the domain.

Final Answer

Domain: *{x|x∈ℝ,x≠3,x≠−3}

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