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Inequalities are essential for comprehending the behavior of rational functions while studying them. This book looks into some inequalities for rational functions that have constrained zeros and predefined poles. We find some intriguing results, specifically about the connection between s-fold zeros at the origin and inequality for polynomials and their polar derivatives. The derived solutions not only sharpen and generalize some well-known inequalities for the derivative of rational functions with prescribed poles, but they also resolve other polynomial inequalities.