The problem is to solve the equation $\frac{2}{p-1} - \frac{1}{p-4} = 0$ for the variable $p$.

1. Problem Description

The problem is to solve the equation $\frac{2}{p-1} - \frac{1}{p-4} = 0$ for the variable $p$.

2. Solution Steps

We are given the equation

$\frac{2}{p-1} - \frac{1}{p-4} = 0$

First, we move the second term to the right side of the equation:

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

Next, we cross-multiply:

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

Expanding both sides, we have

$2p - 8 = p - 1$

Now, we subtract $p$ from both sides:

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

$p - 8 = -1$

Finally, we add 8 to both sides to isolate $p$:

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

$p = 7$

We must also ensure that our solution does not make any of the denominators in the original equation equal to zero.

If $p=7$, then $p-1 = 7-1 = 6 \neq 0$ and $p-4 = 7-4 = 3 \neq 0$. Therefore, $p=7$ is a valid solution.

3. Final Answer

$p = 7$