Answer:
[tex]\{x \in R | x \neq 3\}[/tex]
[tex]\{x \in R | x < 3 \cup x > 3\}[/tex]
[tex]\{x | x > 3, x \in R\} \cup\{x | x < 3, x \in R\}[/tex]
Step-by-step explanation:
To find the domain of a rational expression like [tex]\frac{14x}{x-3}[/tex] 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
[tex]\in[/tex] = element of
| = such that
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[tex]\{x \in R | x \neq 3\}[/tex]
Or you could write it this way
[tex]\{x \in R | x < 3 \cup x > 3\}[/tex]
Or you could write it this way
[tex]\{x | x > 3, x \in R\} \cup\{x | x < 3, x \in R\}[/tex]
