Find the Domain (12x-9)/(6x+3)=2-6/x

Problem

(12*x−9)/(6*x+3)=2−6/x

Solution

1. Identify the denominators in the equation. The domain of an algebraic expression consists of all real numbers except those that make any denominator equal to zero.

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

6*x+3=0

6*x=−3

x=−1/2

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

x=0

4. Exclude these values from the set of all real numbers to define the domain. The domain includes all x such that x≠−1/2 and x≠0

Final Answer

Domain: *{[x∈ℝ,x≠−1/2,x≠0]}

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