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Simplify the rational expression.

[tex]\[ \frac{6x-12}{x^2-4x+4} \][/tex]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. [tex]\(\frac{6x-12}{x^2-4x+4} = \boxed{\phantom{answer}} \)[/tex] (Simplify your answer.)

B. The expression cannot be simplified.


Sagot :

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]