Enter the valups for $$ m, n $$, and $$ p $$ that complete the difference: $$ \frac{7}{x}-\frac{3}{2}=\frac{n-m x}{p x} $$

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We start with the equation

$$
\frac{7}{x} - \frac{3}{2} = \frac{n - m x}{p x}.
$$

**Step 1.** Find a common denominator for the left-hand side. The common denominator for $$ \frac{7}{x} $$ and $$ \frac{3}{2} $$ is $$ 2x $$. Rewrite each term:

$$
\frac{7}{x} = \frac{7 \cdot 2}{2x} = \frac{14}{2x} \quad \text{and} \quad \frac{3}{2} = \frac{3 \cdot x}{2x} = \frac{3x}{2x}.
$$

**Step 2.** Combine the fractions:

$$
\frac{14}{2x} - \frac{3x}{2x} = \frac{14 - 3x}{2x}.
$$

Now, the equation becomes

$$
\frac{14 - 3x}{2x} = \frac{n - m x}{p x}.
$$

**Step 3.** Since the denominators must be equal for the fractions to be identical, and both denominators already contain $$ x $$, equate the remaining constant factors:

$$
2x \quad \text{on the left-hand side must equal} \quad p x \quad \text{on the right-hand side.}
$$

Cancel $$ x $$ (assuming $$ x \neq 0 $$) to obtain

$$
2 = p.
$$

Thus,

$$
p = 2.
$$

**Step 4.** Next, equate the numerators:

$$
14 - 3x = n - m x.
$$

This equation must hold for all values of $$ x $$. Equate the coefficients of like terms:

- The constant term: 
  $$
  14 = n.
  $$
- The coefficient of $$ x $$:
  $$
  -3 = -m \quad \Rightarrow \quad m = 3.
  $$

**Final Answer:**

$$
m = 3, \quad n = 14, \quad p = 2.
$$
$$ m = 3 $$, $$ n = 14 $$, and $$ p = 2 $$.

Enter the valups for \( m, n \), and \( p \) that complete the difference: \( \frac{7}{x}-\frac{3}{2}=\frac{n-m x}{p x} \)

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