https://file.aiquickdraw.com/mathbot/file/1725482331041309nzasv.jpg

The expression in the image is:

\[
\frac{8 - 2x}{x - 3} \div \frac{x - 4}{2x - 6}
\]

To simplify this, we can follow these steps:

### Step 1: Rewrite the division as multiplication.
When dividing by a fraction, we multiply by the reciprocal. So the expression becomes:

\[
\frac{8 - 2x}{x - 3} \times \frac{2x - 6}{x - 4}
\]

### Step 2: Simplify the terms.
- Factor \( 8 - 2x \):  
  \( 8 - 2x = 2(4 - x) \).
- Factor \( 2x - 6 \):  
  \( 2x - 6 = 2(x - 3) \).

So the expression becomes:

\[
\frac{2(4 - x)}{x - 3} \times \frac{2(x - 3)}{x - 4}
\]

### Step 3: Cancel common factors.
- The terms \( x - 3 \) cancel out in both the numerator and the denominator.
- The result is:

\[
2(4 - x) \times \frac{2}{x - 4}
\]

### Step 4: Simplify further.
- Notice that \( 4 - x = -(x - 4) \).
- This gives us:

\[
2(-1) \times \frac{2}{x - 4} = -4 \times \frac{1}{x - 4}
\]

Finally, the expression simplifies to:

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

This is the simplified form of the given expression.

Do you have any questions or would you like further details? Here are some related questions:

1. How do we handle complex fractions in more general cases?
2. What other factoring techniques can be used to simplify expressions?
3. How would the result change if \( x = 4 \)?
4. Can this expression have any undefined points?
5. How do reciprocal rules apply in division of fractions?

**Tip:** Always check if any terms can be factored out and simplified before multiplying or dividing.

Simplify the expression: \( \frac{8 - 2x}{x - 3} \div \frac{x - 4}{2x - 6} \)

Learn how to simplify the rational expression \( \frac{8 - 2x}{x - 3} \div \frac{x - 4}{2x - 6} \) step-by-step. This problem involves key algebraic concepts such as division of fractions, factorization, and simplification. Ideal for students in Grades 8-10.

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