https://file.aiquickdraw.com/mathbot/file/1725597085734gonr80wz.jpg

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?

Please factorize the expression: (5x - 5)/(x^2 + 5x) + 1/(x^2 + 4x) = 4/(x + 5)

Explore how to factorize and solve rational expressions with detailed step-by-step explanations. Learn key concepts such as factoring algebraic expressions, finding common denominators, and applying the fundamental theorem of algebra. Ideal for students in Grades 9-12.

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