Find the Domain (ac)/(cb)=3/2

Problem

(a*c)/(c*b)=3/2

Solution

1. Identify the variables in the expression. The equation involves three variables: a b and c

2. Analyze the denominator of the fraction on the left side. For a rational expression to be defined, the denominator cannot be equal to zero.

3. Set the denominator c*b to be non-zero. This implies that neither c nor b can be zero.

c*b≠0

4. Determine the individual constraints for the variables. Since the product c*b is in the denominator, we must have c≠0 and b≠0

5. Observe that the variable a is in the numerator and has no restrictions from this expression. Therefore, a can be any real number.

6. State the domain in terms of the variables involved. The domain consists of all ordered triples (a,b,c) such that b≠0 and c≠0

Final Answer

Domain:{[(a,b,c)∈ℝ3,b≠0,c≠0]}

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