Find the Domain (a-b)/(a+b+c)=(a-2b+c)/(a-b)

Problem

(a−b)/(a+b+c)=(a−2*b+c)/(a−b)

Solution

1. Identify the denominators in the given equation. For a rational expression to be defined, the denominator cannot be equal to zero.

2. Set the first denominator to be non-zero. The expression (a−b)/(a+b+c) is defined only if a+b+c≠0

3. Set the second denominator to be non-zero. The expression (a−2*b+c)/(a−b) is defined only if a−b≠0

4. Solve the inequality for the second condition. From a−b≠0 we conclude that a≠b

5. Combine the restrictions to define the domain of the equation. The variables a b and c can be any real numbers such that these two conditions are met simultaneously.

Final Answer

Domain={[(a,b,c)∈ℝ3,a+b+c≠0* and *a≠b]}

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