Can someone show me how to do this problem: find the domain and write the set notation (14x)/(x-3)

Question

Can someone show me how to do this problem:

find the domain and write the set notation

`(14x)/(x-3)`

Answer 1

`\ x \\eq 3\`

`\ x < 3 \cup x > 3\`

`\ x > 3, x \in R\ \cup\x`

Explanation:

To find the domain of a rational expression like
`(14x)/(x-3)` you need to find out where the denominator is 0 because you cannot divide by 0

So, take the denominator x - 3 and set it to zero and solve for x

x - 3 = 0

x = 3

So the domain is all real numbers but where x = 3. You can write this in a few different ways in set notation.

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NOTE

R = real numbers

`\in` = element of

| = such that

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`\ x \\eq 3\`

Or you could write it this way

`\ x < 3 \cup x > 3\`

Or you could write it this way

`\x \cup\ x < 3, x \in R\`