Question

Can someone show me how to do this problem:

Answer 1

Answer:

$\{x \in R | x \neq 3\}$

$\{x \in R | x < 3 \cup x > 3\}$

$\{x | x > 3, x \in R\} \cup\{x | x < 3, x \in R\}$

Step-by-step explanation:

To find the domain of a rational expression like $\frac{14x}{x-3}$ 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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$\{x \in R | x \neq 3\}$

Or you could write it this way

$\{x \in R | x < 3 \cup x > 3\}$

Or you could write it this way

$\{x | x > 3, x \in R\} \cup\{x | x < 3, x \in R\}$