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------------------------------------------------ Find the difference. Express your answer in simplest form.

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

To find the difference and express the answer in simplest form, let’s follow these steps:

We need to subtract these two fractions:
[tex]\[
\frac{6s}{s^2 - 4s + 4} - \frac{12}{s^2 - 4s + 4}
\][/tex]

1. Common Denominator: Both fractions already have the same denominator, [tex]\(s^2 - 4s + 4\)[/tex].

2. Combine the Fractions: Since they have a common denominator, we can subtract the numerators directly:

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

3. Simplify the Numerator: Factor the expression [tex]\(6s - 12\)[/tex]:
- Factor out the common factor of 6:
[tex]\[
6s - 12 = 6(s - 2)
\][/tex]

4. Factor the Denominator: The denominator [tex]\(s^2 - 4s + 4\)[/tex] can be factored as:
[tex]\[
s^2 - 4s + 4 = (s - 2)^2
\][/tex]
This is because [tex]\(s^2 - 4s + 4\)[/tex] is a perfect square trinomial.

5. Cancel the Common Factor: The expression now looks like this:
[tex]\[
\frac{6(s - 2)}{(s - 2)^2}
\][/tex]
Since [tex]\(s - 2\)[/tex] is a common factor in both the numerator and the denominator, we can cancel out one [tex]\(s - 2\)[/tex] from each:

[tex]\[
\frac{6}{s - 2}
\][/tex]

Therefore, the simplified form of the expression is:
[tex]\[
\frac{6}{s - 2}
\][/tex]

This is the simplest form of the difference.