College

Simplify the expression to its simplest form.

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

Enter the correct answer in the box below.

[tex]\square[/tex]

Answer :

Sure! Let's simplify the expression step-by-step:

We start with the expression:

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

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

### Step 2: Combine the Fractions
Since the denominators are the same, we can combine the numerators:

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

### Step 3: Factor the Denominator
The denominator [tex]\(s^2 - 4s + 4\)[/tex] can be factored. Notice that it is a perfect square trinomial:

[tex]\[
s^2 - 4s + 4 = (s - 2)^2
\][/tex]

Now the expression becomes:

[tex]\[
\frac{2s - 4}{(s - 2)^2}
\][/tex]

### Step 4: Simplify the Numerator
Factor the numerator:

[tex]\[
2s - 4 = 2(s - 2)
\][/tex]

So the expression becomes:

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

### Step 5: Cancel Common Factors
There is a common factor of [tex]\((s - 2)\)[/tex] in the numerator and denominator. Cancel this factor:

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

So, the simplest form of the given expression is:

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

And that's the final answer!

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