It looks like you've uploaded an image of a math worksheet with several problems, and there's a specific part highlighted in red that seems to be the focus. Let me analyze and solve the problem based on what I can see.
Problem:
The highlighted section shows:
>
Simplify:
> $$
> \frac{2x^2 - 8}{x^2 - 4x + 4}
> $$
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Step-by-step Solution:
We are asked to simplify the rational expression:
$$
\frac{2x^2 - 8}{x^2 - 4x + 4}
$$
---
#### Step 1: Factor the numerator and denominator.
Numerator: $ 2x^2 - 8 $
Factor out the GCF (greatest common factor):
$$
2x^2 - 8 = 2(x^2 - 4)
$$
Now, notice that $ x^2 - 4 $ is a
difference of squares:
$$
x^2 - 4 = (x - 2)(x + 2)
$$
So the numerator becomes:
$$
2(x - 2)(x + 2)
$$
---
Denominator: $ x^2 - 4x + 4 $
This is a
perfect square trinomial:
$$
x^2 - 4x + 4 = (x - 2)^2
$$
---
#### Step 2: Rewrite the expression with factored forms:
$$
\frac{2(x - 2)(x + 2)}{(x - 2)^2}
$$
---
#### Step 3: Cancel common factors.
We can cancel one $ (x - 2) $ from the numerator and denominator:
$$
\frac{2(x + 2)}{x - 2}
$$
(Note: We assume $ x \neq 2 $, because the original denominator would be zero at $ x = 2 $.)
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✔ Final Answer:
$$
\boxed{\frac{2(x + 2)}{x - 2}}
$$
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Let me know if you'd like help with any of the other problems on the worksheet!
Parent Tip: Review the logic above to help your child master the concept of mole conversion practice worksheet.
