Question

select the correct answer.
what is the quotient?
\boxed{\dfrac{x^2 - 4}{(x - 2)(x - 4)}}
a. \\(\dfrac{x + 2}{x - 4}\\)
b. \\(\dfrac{x - 2}{x - 4}\\)
c. \\(\dfrac{x}{x - 2}\\)
d. \\(\dfrac{x + 2}{x - 2}\\)

Explanation:

Step1: Factor the numerator

The numerator \(x^2 - 4\) is a difference of squares, which factors as \((x - 2)(x + 2)\) (since \(a^2 - b^2=(a - b)(a + b)\), here \(a = x\), \(b = 2\)). So the expression becomes \(\frac{(x - 2)(x + 2)}{(x - 2)(x - 4)}\).

Step2: Cancel common factors

We can cancel the common factor \((x - 2)\) from the numerator and the denominator (assuming \(x
eq2\) to avoid division by zero). After canceling, we are left with \(\frac{x + 2}{x - 4}\).

Answer:

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