https://file.aiquickdraw.com/mathbot/file/1730395230716kkrup7s9.jpg

The expression to simplify in your image appears to be:

\[
16 - 6x \left(\frac{4x - 5}{3x - 3}\right) - 36x
\]

Let's go through the simplification step-by-step:

1. **Simplify the fraction \(\frac{4x - 5}{3x - 3}\):**
   - We can factor out \(3\) from the denominator: 
     \[
     \frac{4x - 5}{3(x - 1)}
     \]
   This fraction can't be simplified further because the numerator and denominator have no common factors.

2. **Rewrite the expression with the fraction simplified:**
   \[
   16 - 6x \cdot \frac{4x - 5}{3(x - 1)} - 36x
   \]

3. **Distribute \(-6x\) over \(\frac{4x - 5}{3(x - 1)}\):**
   \[
   -6x \cdot \frac{4x - 5}{3(x - 1)} = \frac{-6x(4x - 5)}{3(x - 1)} = \frac{-24x^2 + 30x}{3(x - 1)}
   \]
   Simplify the fraction by dividing each term in the numerator by \(3\):
   \[
   = \frac{-8x^2 + 10x}{x - 1}
   \]

4. **Rewrite the entire expression with this distributed term:**
   \[
   16 - \frac{8x^2 - 10x}{x - 1} - 36x
   \]

This is now in a simplified form unless you want to go further with a common denominator or further algebraic manipulation. 

Would you like a deeper simplification, or do you have any questions on these steps?

### Follow-up Questions
1. How can we factor more complex polynomials?
2. What are alternative methods to simplify expressions with fractions?
3. When is it useful to find a common denominator in expressions like this?
4. How do we handle expressions with multiple variables differently?
5. What is the difference between simplifying an expression and solving an equation?

### Tip
Always check if the terms in the numerator and denominator can be factored and canceled to make simplification easier.

Simplify the expression: 16 - 6x(4x - 5)/(3x - 3) - 36x

This step-by-step guide simplifies the algebraic expression 16 - 6x(4x - 5)/(3x - 3) - 36x. The solution covers key algebra concepts such as distribution, fraction simplification, and handling expressions with variables. Ideal for high school students in Grades 9-10.

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