The given expression is:

$\frac{3}{x - 2} - \frac{1}{x}$

To simplify or combine these two terms, we need to find a common denominator. The denominators are $x - 2$ and $x$, so the least common denominator (LCD) will be the product of these two: $(x - 2)(x)$.

Now let's rewrite each term with this common denominator:

1. For the first term, $\frac{3}{x - 2}$, we multiply both the numerator and the denominator by $x$: $\frac{3}{x - 2} = \frac{3x}{x(x - 2)}$

2. For the second term, $\frac{1}{x}$, we multiply both the numerator and the denominator by $x - 2$: $\frac{1}{x} = \frac{x - 2}{x(x - 2)}$

Now we can subtract the fractions:

$\frac{3x}{x(x - 2)} - \frac{x - 2}{x(x - 2)} = \frac{3x - (x - 2)}{x(x - 2)}$

Simplify the numerator:

$3x - (x - 2) = 3x - x + 2 = 2x + 2$

So the expression becomes:

$\frac{2x + 2}{x(x - 2)}$

Finally, we can factor out a 2 from the numerator:

$\frac{2(x + 1)}{x(x - 2)}$

Thus, the simplified expression is:

$\frac{2(x + 1)}{x(x - 2)}$

Would you like further details or have any questions?

Here are 5 related questions to expand on this:

1. How can we simplify rational expressions further?
2. What are the steps to find the least common denominator in a fraction problem?
3. How do we handle restrictions on variables, such as when denominators become zero?
4. Can you apply this process to a more complex expression?
5. How do you solve equations involving rational expressions?

Tip: Always check for possible restrictions by ensuring the denominator doesn’t equal zero (in this case, $x \neq 0$ and $x \neq 2$).