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The problem asks to subtract the two rational expressions:

\[
\frac{3x}{x+5} - \frac{3x - 6}{2x + 10}
\]

### Step 1: Simplify the second denominator.
Notice that \(2x + 10\) can be factored:
\[
2x + 10 = 2(x + 5)
\]

Thus, the expression becomes:
\[
\frac{3x}{x + 5} - \frac{3x - 6}{2(x + 5)}
\]

### Step 2: Find a common denominator.
The common denominator between \(x + 5\) and \(2(x + 5)\) is \(2(x + 5)\). We need to adjust the first fraction by multiplying both its numerator and denominator by 2:
\[
\frac{3x}{x + 5} = \frac{2(3x)}{2(x + 5)} = \frac{6x}{2(x + 5)}
\]

Now the expression is:
\[
\frac{6x}{2(x + 5)} - \frac{3x - 6}{2(x + 5)}
\]

### Step 3: Subtract the numerators.
Now that the denominators are the same, we can subtract the numerators:
\[
\frac{6x - (3x - 6)}{2(x + 5)} = \frac{6x - 3x + 6}{2(x + 5)} = \frac{3x + 6}{2(x + 5)}
\]

### Step 4: Simplify the numerator.
The numerator \(3x + 6\) can be factored:
\[
3x + 6 = 3(x + 2)
\]

Thus, the expression becomes:
\[
\frac{3(x + 2)}{2(x + 5)}
\]

This is the simplified form of the expression.

Would you like more details or further clarification? 

### Related Questions:
1. How do you find a common denominator for rational expressions?
2. What steps are involved in factoring polynomials?
3. Can you subtract fractions with different denominators without finding a common denominator?
4. How do you simplify a rational expression?
5. What are the general strategies for solving problems with rational expressions?

### Tip:
Always look for opportunities to factor expressions to simplify rational functions, as this often makes common denominators and cancellation easier.

Subtract the rational expressions: (3x/(x+5)) - ((3x-6)/(2x+10)) and simplify.

Learn how to subtract and simplify rational expressions like (3x/(x+5)) - ((3x-6)/(2x+10)). This solution demonstrates factoring and finding common denominators step by step, suitable for students in Grades 9-10.

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