The expression to factor is:

\[
\frac{4(x + 3)}{(x + 1)(x + 5)}
\]

In this case, the numerator \(4(x + 3)\) is already factored, and the denominator \((x + 1)(x + 5)\) consists of two linear terms.

Since there are no common factors between the numerator and the denominator, the expression is already in its simplest form.

Thus, the factored form of the expression is:

\[
\frac{4(x + 3)}{(x + 1)(x + 5)}
\]

This is as far as it can be factorized.

Would you like further clarification?

Here are 5 related questions:
1. How do you simplify algebraic fractions further if there are common factors?
2. What happens when there is a quadratic expression in the denominator?
3. How do you perform long division for algebraic expressions?
4. Can you factorize \(x^2 + 5x + 6\) using common factorization techniques?
5. What are partial fractions, and how do they relate to expressions like this?

**Tip:** Always check for common factors between the numerator and denominator when simplifying rational expressions!

Learn how to factor the rational expression 4(x+3)/(x+1)(x+5) by identifying the numerator and denominator terms. Explore key algebraic concepts, including factorization and simplification of rational expressions. Suitable for students in Grades 9-12.

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