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

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

• A. 2(x + 2)
• B. 2(x + 4)
• C. 2(x - 4)
• D. 4(x + 4)

Answer: (A)

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

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