Find the Domain 2/(21x)+4/(15x^2)

Problem

2/(21*x)+4/(15*x2)

Solution

1. Identify the denominators in the expression. The denominators are 21*x and 15*x2

2. Set each denominator equal to zero to find the values that must be excluded from the domain, as division by zero is undefined.

3. Solve the first equation 21*x=0 Dividing both sides by 21 gives x=0

4. Solve the second equation 15*x2=0 Dividing both sides by 15 gives x2=0 which implies x=0

5. Determine the domain by excluding the values found. The only value that makes the expression undefined is x=0

6. Express the domain in interval notation or set-builder notation.

Final Answer

Domain: *(−∞,0)∪(0,∞)

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