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

1. Problem Description

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

2. Solution Steps

First, we add $\frac{1}{p-4}$ to both sides of the equation:

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

Next, we cross-multiply to eliminate the fractions:

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

Distribute on both sides:

$2p - 8 = p - 1$

Subtract $p$ from both sides:

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

$p - 8 = -1$

Add $8$ to both sides:

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

$p = 7$

We must check that this solution is valid, i.e., that it does not make any denominator 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

$p = 7$