Answer :

To solve the problem of finding the difference and expressing it in its simplest form, let's break it down step by step.

You are given two fractions with the same denominator:

1. [tex]\(\frac{6s}{s^2 - 4s + 4}\)[/tex]
2. [tex]\(\frac{12}{s^2 - 4s + 4}\)[/tex]

### Step 1: Recognize the Common Denominator
The denominators of both fractions are the same: [tex]\(s^2 - 4s + 4\)[/tex]. This allows us to easily combine the fractions into one.

### Step 2: Subtract the Numerators
Since the denominators are the same, you can subtract the numerators directly:

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

### Step 3: Simplify the Expression
Now, you can simplify the expression [tex]\(\frac{6s - 12}{s^2 - 4s + 4}\)[/tex].

First, factor the numerator:
- The numerator is [tex]\(6s - 12\)[/tex].
- You can factor out a 6: [tex]\(6(s - 2)\)[/tex].

The denominator [tex]\(s^2 - 4s + 4\)[/tex] can be rewritten as:
- Notice that it can be factored as: [tex]\((s - 2)(s - 2)\)[/tex] or [tex]\((s - 2)^2\)[/tex].

Now, the expression becomes:
[tex]\[
\frac{6(s - 2)}{(s - 2)^2}
\][/tex]

### Step 4: Simplify Further by Canceling Out Common Factors
Since both the numerator and denominator have [tex]\((s - 2)\)[/tex], you can cancel one [tex]\((s - 2)\)[/tex] from the numerator and the denominator:

[tex]\[
\frac{6(s - 2)}{(s - 2)^2} = \frac{6}{s - 2}
\][/tex]

This is the simplest form of the expression.

### Final Answer
So, the difference expressed in its simplest form is:
[tex]\[
\frac{6}{s - 2}
\][/tex]

Thanks for taking the time to read Find the difference Express your answer in simplest form tex frac 6s s 2 4s 4 frac 12 s 2 4s 4 tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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