To simplify the rational expression [tex]\(\frac{6x - 12}{x^2 - 4x + 4}\)[/tex], follow these steps:
1. Identify the Numerator and Denominator:
The numerator is [tex]\(6x - 12\)[/tex].
The denominator is [tex]\(x^2 - 4x + 4\)[/tex].
2. Factor the Numerator and Denominator:
Let's start with the numerator [tex]\(6x - 12\)[/tex]:
Factor out the common term:
[tex]\[
6x - 12 = 6(x - 2)
\][/tex]
Now, for the denominator [tex]\(x^2 - 4x + 4\)[/tex]:
Recognize it as a perfect square trinomial:
[tex]\[
x^2 - 4x + 4 = (x - 2)^2
\][/tex]
3. Rewrite the Rational Expression:
Substitute the factored forms of the numerator and the denominator back into the expression:
[tex]\[
\frac{6x - 12}{x^2 - 4x + 4} = \frac{6(x - 2)}{(x - 2)^2}
\][/tex]
4. Simplify the Expression:
Observe that both the numerator and the denominator have a common factor of [tex]\(x - 2\)[/tex]. Cancel this common factor:
[tex]\[
\frac{6(x - 2)}{(x - 2)^2} = \frac{6}{x - 2}
\][/tex]
Hence, the simplified form of the rational expression is:
[tex]\[
\frac{6x - 12}{x^2 - 4x + 4} = \frac{6}{x - 2}
\][/tex]
Select Choice A and fill in the answer box with [tex]\(\frac{6}{x - 2}\)[/tex]:
A. [tex]\(\frac{6x - 12}{x^2 - 4x + 4} = \frac{6}{x - 2}\)[/tex]
