The expression in the image is:

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

Let's work through the factorization and simplification step by step.

Step 1: Factorizing the denominators

1. $x^2 + 5x = x(x + 5)$
2. $x^2 + 4x = x(x + 4)$
3. $x + 5$ is already factored.

Step 2: Factorizing the numerators

1. $5x - 5 = 5(x - 1)$
2. $1$ remains unchanged.

Simplified expression:

$\frac{5(x - 1)}{x(x + 5)} + \frac{1}{x(x + 4)} = \frac{4}{x + 5}$

Next, we will find a common denominator and proceed with solving this. Would you like to continue with these steps?