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Examples -> Algebra -> Polynomials -> Division of polynomial

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[Source: MathReference: Generic Math Textbook]

Simplify the following expression:

$(\frac{\frac{a}{b} + \frac{b}{a}}{\frac{a}{b} - \frac{b}{a}} + \frac{1}{1 + \frac{b}{a}} - \frac{1}{1 - \frac{b}{a}}) : \frac{1 - \frac{a - 3 b}{a + b}}{\frac{3 a + b}{a - b} - 3}$