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The given expression is:

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

To simplify this expression, follow these steps:

### Step 1: Factor the denominator
Factor the greatest common factor (GCF) from the denominator. The terms in the denominator are \(16w^2\) and \(-40w\), so the GCF is \(8w\).

\[
16w^2 - 40w = 8w(2w - 5)
\]

Now the expression becomes:

\[
\frac{-48w}{8w(2w - 5)}
\]

### Step 2: Simplify the fraction
Now, cancel out the common factor of \(w\) from the numerator and denominator, and divide both by the GCF \(8\).

\[
\frac{-48w}{8w(2w - 5)} = \frac{-6}{2w - 5}
\]

### Final Answer:
\[
\frac{-6}{2w - 5}
\]

Let me know if you'd like further clarifications or more details!

Here are 5 related questions to practice:
1. How would you simplify \(\frac{20x}{4x^2 - 8x}\)?
2. What happens when the numerator and denominator have no common factors?
3. Can you simplify \(\frac{-10y}{5y - 2}\)?
4. How do you factor out the GCF from a trinomial expression?
5. Can you simplify \(\frac{9w^2}{3w(3w + 7)}\)?

**Tip:** Always look for the greatest common factor (GCF) when simplifying rational expressions. This can often help in reducing the expression faster.

Simplify the expression: -48w / (16w^2 - 40w).

Simplify the rational expression -48w / (16w^2 - 40w) using algebraic methods, including factoring out the greatest common factor (GCF) and canceling terms. This detailed step-by-step solution is ideal for students in Grades 9-11, covering core concepts like factoring and rational expressions.

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