Partial Fraction Decomposition with Linear Factors (Interactive)

This example demonstrates how to perform partial fraction decomposition for rational functions whose denominator factors are linear. It visually and algebraically verifies that the decomposed form matches the original expression for randomly generated (or user-specified) parameters. Key concepts include partial fraction decomposition, representation of rational functions via linear factors, solving for unknown coefficients, and validating algebraic identities; the setup also supports function-graph intuition tied to logarithmic-type behavior and basic calculus viewpoints. Construction highlights from the GeoGebra commands and objects: it uses Random / RandomDiscrete to generate parameters (a, b, c, d, f, g, h, p, q, etc.), If to apply conditional logic during setup, Polynomial to build the symbolic expressions, and Textfield plus a set of text objects (text1–text8) to display intermediate steps and results. Max and Min are used to control or filter parameter ranges. The interactive workflow relies on InputBox1–InputBox4 for parameter entry and buttons (button1, button2) to trigger generation/verification, with maxP/maxQ and correctA/correctB used to constrain searches and check coefficient correctness. Suitable for advanced high school, exam prep, and introductory university courses focused on algebraic manipulation of rational functions and their connection to function analysis.