Find the Domain 2/(x-2)=8/(x+13)

Problem

2/(x−2)=8/(x+13)

Solution

1. Identify the denominators in the equation. The expressions in the denominators are x−2 and x+13

2. Set each denominator to be non-zero, as division by zero is undefined in the set of real numbers.

3. Solve the first inequality x−2≠0 to find that x≠2

4. Solve the second inequality x+13≠0 to find that x≠−13

5. Combine these restrictions to define the domain as all real numbers except x=2 and x=−13

Final Answer

Domain={[x∈ℝ,x≠2,x≠−13]}

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