Find the Domain f(x)=1/x+5/(x-3)

Problem

ƒ(x)=1/x+5/(x−3)

Solution

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

2. Set the first denominator equal to zero to find the first excluded value.

x=0

3. Set the second denominator equal to zero to find the second excluded value.

x−3=0

4. Solve for x in the second equation.

x=3

5. State the domain by excluding these values from the set of all real numbers. In interval notation, this is the union of intervals not containing 0 and 3

(−∞,0)∪(0,3)∪(3,∞)

Final Answer

Domain:(−∞,0)∪(0,3)∪(3,∞)

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