The problem is to add the expression $\frac{11x}{5x-4}$ to $4$ and simplify the result.

1. Problem Description

The problem is to add the expression $\frac{11x}{5x-4}$ to $4$ and simplify the result.

2. Solution Steps

First, we need to find a common denominator to add the two terms. The common denominator is $5x-4$. We can rewrite $4$ as $\frac{4(5x-4)}{5x-4}$. Now we can add the two terms:

$\frac{11x}{5x-4} + 4 = \frac{11x}{5x-4} + \frac{4(5x-4)}{5x-4}$

Next, we combine the numerators:

$\frac{11x + 4(5x-4)}{5x-4}$

Distribute the $4$ in the numerator:

$\frac{11x + 20x - 16}{5x-4}$

Combine like terms in the numerator:

$\frac{31x - 16}{5x-4}$

3. Final Answer

$\frac{31x-16}{5x-4}$