Find the Domain x/(3x+4)

Problem

x/(3*x+4)

Solution

1. Identify the condition for the domain of a rational function. A rational function is defined for all real numbers except where the denominator is equal to zero.

2. Set the denominator equal to zero to find the excluded values.

3*x+4=0

3. Solve for x by subtracting 4 from both sides.

3*x=−4

4. Divide both sides by 3 to isolate x

x=−4/3

5. State the domain as all real numbers except the value that makes the denominator zero. In interval notation, this excludes −4/3

Final Answer

Domain: *(−∞,−4/3)∪(−4/3,∞)

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