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.