Simplify \( \frac{4x^2 - 16}{2x - 4} \).

To simplify the expression ( \frac{4x^2 - 16}{2x - 4} ), we begin by factoring both the numerator and the denominator.

The numerator, ( 4x^2 - 16 ), can be recognized as a difference of squares. It can be factored as follows:

[

4(x^2 - 4) = 4(x - 2)(x + 2)

]

Next, the denominator ( 2x - 4 ) can be factored by taking out the common factor of 2:

[

2(x - 2)

]

Putting it all together, the original expression now looks like this:

[

\frac{4(x - 2)(x + 2)}{2(x - 2)}

]

We can now cancel the common factor ( (x - 2) ) from the numerator and the denominator, assuming ( x \neq 2 ) to avoid division by zero. This simplifies our expression to:

[

\frac{4(x + 2)}{2}

]

When we divide ( 4 ) by ( 2 ), we get ( 2 ). Therefore, the