The expression you provided appears to be a combination of algebraic terms. Let me rewrite it clearly:

\[
\frac{a^2b^2}{a^2 + b^2} + 1
\]

Now, let's simplify it step by step:

1. The expression is a sum of two terms: \(\frac{a^2b^2}{a^2 + b^2}\) and \(1\).
2. To add these two terms, we'll need a common denominator.

\[
\frac{a^2b^2}{a^2 + b^2} + 1 = \frac{a^2b^2}{a^2 + b^2} + \frac{a^2 + b^2}{a^2 + b^2}
\]

3. Combine the fractions:

\[
\frac{a^2b^2 + a^2 + b^2}{a^2 + b^2}
\]

This is the simplified form of the given expression.

Would you like more details or have any questions? Here are 5 related questions for further exploration:

1. How do you factor \(a^2b^2 + a^2 + b^2\) if possible?
2. What happens to the expression when \(a = b\)?
3. Can this expression be solved for specific values of \(a\) and \(b\)?
4. What would the behavior of the expression be as \(a\) or \(b\) approaches infinity?
5. How does the expression change if you subtract \(1\) instead of adding it?

**Tip:** When working with algebraic fractions, finding a common denominator helps to simplify and combine the terms efficiently.

Learn how to simplify the algebraic expression a²b² / (a² + b²) + 1 step by step. This problem covers key algebraic concepts like rational expressions and fraction addition. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation