The expression you've provided is:

\[
\frac{1}{x+y} + \frac{x+y}{x^3 + y^3}
\]

To simplify this expression, let's combine the two fractions:

\[
\frac{1}{x+y} + \frac{x+y}{x^3 + y^3} = \frac{(x^3 + y^3) + (x+y)^2}{(x+y)(x^3 + y^3)}
\]

This is the simplified form of the expression. The numerator now includes the sum of \( x^3 + y^3 \) and \( (x+y)^2 \).

Would you like a more detailed explanation of how this simplification works?

Here are five related questions you might find interesting:
1. How can you factor \( x^3 + y^3 \) using algebraic identities?
2. What happens if \( x = y \) in the given expression?
3. How do you simplify the expression if \( x + y = 0 \)?
4. What is the geometric interpretation of the expression in terms of coordinates?
5. Can you find the partial derivatives of the expression with respect to \( x \) and \( y \)?

**Tip:** When working with fractions involving polynomials, it's often helpful to factor common terms in the numerator and denominator to simplify the expression.

Learn how to simplify the fraction expression 1/(x+y) + (x+y)/(x^3+y^3) with a step-by-step explanation. This problem involves combining fractions and simplifying polynomial expressions. Suitable for advanced high school students.

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