The given expression is:

\[
\frac{b^2}{b^2 + (s + a)^2} \times \frac{1}{b}
\]

We can simplify this step by step:

1. Rewrite the expression as:
\[
\frac{b^2}{b(b^2 + (s + a)^2)}
\]

2. Now, we can simplify \(b^2\) with \(b\) in the denominator:
\[
\frac{b}{b^2 + (s + a)^2}
\]

So the simplified expression is:

\[
\frac{b}{b^2 + (s + a)^2}
\]

Would you like a detailed explanation of how this simplification works, or do you have any questions?

Here are 5 related questions for further exploration:
1. How would the expression change if the exponent on \(b^2\) was increased to \(b^3\)?
2. How would you differentiate this expression with respect to \(a\)?
3. What happens if \(a = 0\) in the given expression?
4. How does the expression behave as \(b \to 0\)?
5. How does this expression relate to a standard rational function?

**Tip**: When simplifying fractions, always look for common terms in the numerator and denominator that can cancel out.

Learn how to simplify the rational expression b² / (b² +(s+a)²) * 1/b with a step-by-step guide. This problem covers important algebraic concepts, including rational expressions and simplification techniques. Ideal for students in Grades 9-12.

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