https://file.aiquickdraw.com/mathbot/file/1727028546937gk93ok6u.jpg

The expression in the image appears to be:

\[
\frac{16w^2 - 48w}{-40w}
\]

We can simplify this expression by following these steps:

### Step 1: Factor the numerator
The numerator is \(16w^2 - 48w\). We can factor out the greatest common factor (GCF) of 16w:

\[
16w^2 - 48w = 16w(w - 3)
\]

So the expression becomes:

\[
\frac{16w(w - 3)}{-40w}
\]

### Step 2: Simplify the fraction
We can now simplify by canceling the common factor of \(w\) (assuming \(w \neq 0\)) and reducing the numeric fraction:

\[
\frac{16w(w - 3)}{-40w} = \frac{16(w - 3)}{-40} = \frac{-16(w - 3)}{40}
\]

We can simplify the numeric fraction \( \frac{-16}{40} \) by dividing both the numerator and the denominator by 8:

\[
\frac{-16}{40} = \frac{-2}{5}
\]

### Final Simplified Expression:
\[
\frac{-2(w - 3)}{5}
\]

Or equivalently:

\[
-\frac{2(w - 3)}{5}
\]

Would you like more details or have any questions about the steps?

Here are 5 questions to explore further:

1. What happens if \(w = 0\) in the original expression?
2. How would the expression change if the numerator was \(16w^2 + 48w\)?
3. How do we factor expressions like \(16w^2 - 48w\) in general?
4. Why do we cancel common factors between the numerator and denominator?
5. How does simplification of complex fractions help in solving equations?

**Tip**: Always check for common factors before simplifying expressions; it makes the process easier and reduces the chance of errors.

Simplify the expression \( \frac{16w^2 - 48w}{-40w} \)

Learn how to simplify the algebraic expression \( \frac{16w^2 - 48w}{-40w} \). This step-by-step solution covers factoring quadratic expressions and simplifying fractions. Suitable for students in Grades 9-10.

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