We are asked to solve the equation $\frac{2}{p-1} - \frac{1}{p-4} = 0$ for $p$.

1. Problem Description

We are asked to solve the equation $\frac{2}{p-1} - \frac{1}{p-4} = 0$ for $p$.

2. Solution Steps

First, we rewrite the equation:

$\frac{2}{p-1} = \frac{1}{p-4}$

Now, we can cross-multiply:

$2(p-4) = 1(p-1)$

Expanding both sides, we get:

$2p - 8 = p - 1$

Next, we isolate $p$ by subtracting $p$ from both sides:

$2p - p - 8 = p - p - 1$

$p - 8 = -1$

Finally, we add 8 to both sides:

$p - 8 + 8 = -1 + 8$

$p = 7$

We need to check if $p=7$ is a valid solution by ensuring that the denominators are not zero.

When $p=7$, $p-1 = 7-1 = 6 \neq 0$ and $p-4 = 7-4 = 3 \neq 0$. Thus, $p=7$ is a valid solution.

3. Final Answer

$p = 7$