Find the Domain ((6-2x)/(2x+8))÷(9-3x)

Problem

(6−2*x)/(2*x+8)/(9−3*x)

Solution

1. Identify the constraints for the domain of a rational expression. The domain consists of all real numbers except those that make any denominator in the expression equal to zero.

2. Set the denominator of the internal fraction to zero to find the first excluded value.

2*x+8=0

2*x=−8

x=−4

3. Set the denominator of the entire expression to zero to find the second excluded value.

9−3*x=0

−3*x=−9

x=3

4. Combine the restrictions. The variable x cannot be −4 or 3 In interval notation, this excludes these two points from the set of all real numbers.

Final Answer

Domain:(−∞,−4)∪(−4,3)∪(3,∞)

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