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Multiplication and Division of Rational Expressions

Multiplication and Division of Rational Expressions
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2020-05-12 21:41
FunctionInequalityGraphing
This GeoGebra example demonstrates the multiplication and division of rational expressions (fractions with polynomial numerators and denominators) through an interactive interface. It visually shows step-by-step simplification and factorization of the resulting expressions. Core math concepts include the multiplication rule (multiply numerators and denominators), division as multiplying by the reciprocal, factoring polynomials, and canceling common factors to obtain simplified forms. The construction uses Textfield and InputBox components for user input of two rational expressions, Simplify and Factor commands to process the inputs, and If commands to validate entries and compute the product (Prod) and quotient (Quot). Objects include P, Q, R, S, A, B, C, D, and multiple text labels (text1–text9) to display results. This resource is suitable for high school algebra or pre-calculus students, as well as teachers for classroom demonstrations or self-paced practice, enabling immediate verification of algebraic manipulation skills.

GeoGebra Commands & Parameters

  1. Textfield(P) → InputBox1
  2. Textfield(Q) → InputBox2
  3. Textfield(R) → InputBox3
  4. Textfield(S) → InputBox4
  5. Simplify((P(x) / Q(x) * R(x) / S(x))) → Prod
  6. Simplify((P(x) / Q(x) * S(x) / R(x))) → Quot
  7. Factor(P) → h
  8. Factor(Q) → p
  9. Factor(R) → q
  10. Factor(S) → r
  11. If(e ≟ -1, text7, text9) → text8
  12. If(e ≟ -1, text5, text6) → text0

AI Drawing Prompt Reference

Create an interactive educational interface for demonstrating multiplication and division of rational expressions. Place four input boxes in the center for entering the numerators and denominators of two rational expressions. Below the inputs, show two main result areas: one displaying the simplified product of the two expressions, and the other showing the simplified quotient (first divided by second, i.e., multiplied by the reciprocal). Next to each result, display the factored forms of the original polynomials, breaking each numerator and denominator into irreducible factors. Include conditional text prompts that show an error message when inputs are invalid, otherwise show the correct results. The layout should be clean and suitable for high school algebra demonstrations.
The prompt above was compiled from the original drawing commands and is for reference only.