The given expression is:

\[
\frac{(3x-2)(x-5)}{(2x-5)(x-5)}
\]

We will first simplify both the numerator and the denominator.

### Step 1: Expand the numerator
The numerator is \((3x - 2)(x - 5)\).
\[
(3x - 2)(x - 5) = 3x(x - 5) - 2(x - 5)
\]
\[
= 3x^2 - 15x - 2x + 10
\]
\[
= 3x^2 - 17x + 10
\]

### Step 2: Expand the denominator
The denominator is \((2x - 5)(x - 5)\).
\[
(2x - 5)(x - 5) = 2x(x - 5) - 5(x - 5)
\]
\[
= 2x^2 - 10x - 5x + 25
\]
\[
= 2x^2 - 15x + 25
\]

### Step 3: Combine the results
Now, the expression becomes:
\[
\frac{3x^2 - 17x + 10}{2x^2 - 15x + 25}
\]

This is the simplified form of the expression. It doesn't factor further, so this is the final answer.

Would you like more details on any of these steps?

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Here are five related questions for further practice:
1. How would the expression change if both \(x - 5\) terms were replaced with \(x + 5\)?
2. Can you factor both the numerator and the denominator?
3. How do you find the domain of this rational expression?
4. How would you solve the equation if this expression were set equal to zero?
5. What happens if you substitute \(x = 5\) into the original expression?

**Tip:** When simplifying algebraic expressions, always check if there are common factors that can be canceled out!

The query submitted by the user: (3x-2)*(x-5):(2x-5)*(x-5)

This detailed solution explains how to simplify the rational expression (3x-2)(x-5)/(2x-5)(x-5) using polynomial expansion and rational expression techniques. Follow a step-by-step process suitable for students in Grades 8-10.

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