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

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:** \[ \boxed{\displaystyle \frac{-1}{2p-5}} \]