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 \(x \neq 2\)).

Learn how to simplify the rational expression 3/(x-2) - 1/x using the least common denominator (LCD). This solution includes detailed steps for finding the LCD, rewriting terms, and simplifying the resulting expression. Perfect for students in Grades 9-10 studying rational expressions in algebra.

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