Let's simplify the expression step by step:

The given expression is:

\[
2x - 18 - \frac{(2x - 18)}{3}
\]

### Step 1: Simplify the fraction

We can split the term inside the fraction, but in this case, it's easier to just keep the expression as it is and work step by step.

### Step 2: Get a common denominator

To subtract \(\frac{(2x - 18)}{3}\) from \(2x - 18\), let's rewrite \(2x - 18\) with a denominator of 3:

\[
2x - 18 = \frac{3(2x - 18)}{3}
\]

This gives us:

\[
\frac{3(2x - 18)}{3} - \frac{(2x - 18)}{3}
\]

### Step 3: Combine the fractions

Now that both terms have the same denominator, we can subtract the numerators:

\[
\frac{3(2x - 18) - (2x - 18)}{3}
\]

### Step 4: Simplify the numerator

Distribute and combine like terms:

\[
3(2x - 18) = 6x - 54
\]
\[
6x - 54 - (2x - 18) = 6x - 54 - 2x + 18 = 4x - 36
\]

### Step 5: Write the final expression

Now, the expression becomes:

\[
\frac{4x - 36}{3}
\]

This is the simplified form of the given expression.

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Let me know if you would like further details or have any questions. Here are some related questions:

1. How do you handle more complex fractions in algebraic expressions?
2. Can this expression be factored further?
3. How do you apply the distributive property to more complex polynomials?
4. How does solving for \( x \) change with this simplified expression?
5. Can this type of expression appear in word problems, and how would you interpret it?

**Tip**: Always simplify algebraic fractions by getting a common denominator before combining terms!

Learn how to simplify the algebraic expression 2x - 18 - (2x - 18)/3 using common denominator rules and the distributive property. This problem walks through each step of the process, making it ideal for students in Grades 8-10.

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