To solve the equation:

$\frac{4}{x - 4} + \frac{2}{x + 1} = \frac{5x}{x^2 - 3x - 4}$

Step 1: Factor the Denominator on the Right Side

The denominator on the right side is $x^2 - 3x - 4$. We can factor this as: $x^2 - 3x - 4 = (x - 4)(x + 1)$

So, the equation becomes: $\frac{4}{x - 4} + \frac{2}{x + 1} = \frac{5x}{(x - 4)(x + 1)}$

Step 2: Find a Common Denominator

The common denominator for all terms is $(x - 4)(x + 1)$. Rewrite each term with this denominator: $\frac{4(x + 1)}{(x - 4)(x + 1)} + \frac{2(x - 4)}{(x - 4)(x + 1)} = \frac{5x}{(x - 4)(x + 1)}$

Step 3: Expand and Combine Terms in the Numerator

Expanding each term in the numerator:

1. $4(x + 1) = 4x + 4$
2. $2(x - 4) = 2x - 8$

So, the equation becomes: $\frac{4x + 4 + 2x - 8}{(x - 4)(x + 1)} = \frac{5x}{(x - 4)(x + 1)}$

Combine like terms in the numerator: [ \frac{(