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To solve the given expression:

\[
\frac{3x}{x + 4} - \frac{3}{x - 8}
\]

we follow these steps:

### Step 1: Find a common denominator
The denominators are \(x + 4\) and \(x - 8\). The least common denominator (LCD) will be the product of both, i.e.:

\[
(x + 4)(x - 8)
\]

### Step 2: Rewrite both fractions with the LCD
We rewrite both fractions so they have the same denominator:

\[
\frac{3x}{x + 4} = \frac{3x(x - 8)}{(x + 4)(x - 8)}
\]
\[
\frac{3}{x - 8} = \frac{3(x + 4)}{(x - 8)(x + 4)}
\]

### Step 3: Subtract the numerators
Now that both fractions have the same denominator, we subtract the numerators:

\[
\frac{3x(x - 8) - 3(x + 4)}{(x + 4)(x - 8)}
\]

### Step 4: Expand the numerators
Expand the terms in the numerator:

\[
3x(x - 8) = 3x^2 - 24x
\]
\[
3(x + 4) = 3x + 12
\]

Thus, the expression becomes:

\[
\frac{(3x^2 - 24x) - (3x + 12)}{(x + 4)(x - 8)} = \frac{3x^2 - 24x - 3x - 12}{(x + 4)(x - 8)}
\]

### Step 5: Simplify the numerator
Combine like terms in the numerator:

\[
3x^2 - 24x - 3x - 12 = 3x^2 - 27x - 12
\]

### Final Answer:
The expression simplifies to:

\[
\frac{3x^2 - 27x - 12}{(x + 4)(x - 8)}
\]

Let me know if you need any more details or if you'd like further clarification.

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Here are 5 related questions for practice:

1. How would you simplify \(\frac{2x}{x + 1} + \frac{5}{x - 3}\)?
2. What is the common denominator for \(\frac{x^2}{x - 2}\) and \(\frac{4}{x + 5}\)?
3. How do you simplify \(\frac{5x}{x - 7} - \frac{4}{x + 2}\)?
4. Can you factor the expression \(x^2 - 27x - 12\) further?
5. How do you perform operations with fractions that involve variables in the denominators?

### Tip:
When subtracting or adding rational expressions, always start by finding the least common denominator (LCD) before combining the fractions.

Perform the operation and combine to one fraction: (3x / (x + 4)) - (3 / (x - 8))

Learn how to subtract rational expressions like (3x / (x + 4)) - (3 / (x - 8)) by finding a common denominator and simplifying. This algebra problem covers key topics such as LCD, expanding expressions, and combining fractions.

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