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The given expression is:

\[
\frac{(2x - 11)(3x - 17)}{(2x - 11)(3x - 5)}
\]

### Steps to simplify:

1. **Identify the common factors**: 
   Both the numerator and the denominator contain the factor \( (2x - 11) \).
   
2. **Cancel out the common factor**: 
   Since \( (2x - 11) \) appears in both the numerator and the denominator, it can be canceled out.

This leaves us with:

\[
\frac{(3x - 17)}{(3x - 5)}
\]

Therefore, the expression simplifies to:

\[
\frac{3x - 17}{3x - 5}
\]

### Correct Answer:
The simplified expression is:

\[
\boxed{\frac{3x - 17}{3x - 5}}
\]

Would you like more details, or have any questions on this simplification?

### 5 Related Questions:
1. How do you factor quadratic expressions to find common factors?
2. What happens if there are no common factors between the numerator and denominator?
3. How do you simplify rational expressions with more complex terms?
4. What are the conditions under which you cannot cancel terms in rational expressions?
5. How can this simplification technique be applied to more complex algebraic fractions?

### Tip:
Always check if any terms in the denominator could lead to division by zero, as they need to be excluded from the domain of the function.

Divide out all of the common factors to simplify the function: ((2x - 11)(3x - 17)) / ((2x - 11)(3x - 5))

Learn how to simplify the rational expression ((2x - 11)(3x - 17)) / ((2x - 11)(3x - 5)) by canceling out common factors. This problem covers key algebraic concepts like rational expressions and simplification techniques. Suitable for students in Grades 9-11.

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