Simplify the rational expression. $$ \frac{-8 p}{16 p^{2}-40 p}=\square $$

Question

UpStudy AI · Accepted Answer

To simplify the rational expression:

$$
\frac{-8p}{16p^2 - 40p}
$$

**Step 1: Factor the denominator.**

The denominator $$16p^2 - 40p$$ can be factored by taking out the greatest common factor (GCF), which is $$8p$$:

$$
16p^2 - 40p = 8p(2p) - 8p(5) = 8p(2p - 5)
$$

**Step 2: Rewrite the expression with the factored denominator.**

$$
\frac{-8p}{16p^2 - 40p} = \frac{-8p}{8p(2p - 5)}
$$

**Step 3: Simplify by canceling the common factors.**

Cancel the $$8p$$ in the numerator and the denominator:

$$
\frac{-8p}{8p(2p - 5)} = \frac{-1}{2p - 5}
$$

**Final Answer:**

$$
\boxed{\displaystyle \frac{-1}{2p-5}}
$$
$$ \frac{-1}{2p - 5} $$

Simplify the rational expression.