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The given mathematical expression simplifies to:

\[
\frac{a \cdot \sqrt{a b} \cdot (a - b)}{2 \cdot \sqrt{b \cdot (a - 1)} \cdot (a + \sqrt{a b})}
\]

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Here are 5 related questions:
1. How can we further simplify the numerator or denominator of this expression?
2. What are the possible values for \(a\) and \(b\) to ensure the expression is defined?
3. How does the square root term in the expression influence the solution for \(a\) and \(b\)?
4. Can this expression be factorized in any meaningful way?
5. What would happen to the expression if \(b = 1\)?

**Tip**: To simplify such expressions efficiently, identifying common factors and terms involving square roots early can help streamline the process.

Simplify the given mathematical expression: (sqrt(ab) - ab/(a + sqrt(ab))) * (2(sqrt(ab - b))/(a - b))

Learn how to simplify a complex algebraic expression involving radicals, fractions, and binomials, such as (sqrt(ab) - ab/(a + sqrt(ab))) * (2(sqrt(ab - b))/(a - b)). This solution explores core concepts like radicals and algebraic fraction operations. Suitable for students in Grades 11-12.

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