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Simplifying Rational Expressions and Stating Restrictions by cemccourseware

Simplifying Rational Expressions and Stating Restrictions by cemccourseware
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2019-04-10 21:44
FunctionCoordinate Geometry
This example demonstrates how to simplify rational expressions and state their restrictions. Key mathematical concepts include the simplification of rational expressions and determining their domain. Using GeoGebra commands such as Element, UnicodeToLetter, LaTeX, and Text, students can understand how to manipulate rational expressions. Suitable for middle school and above students.

GeoGebra Commands & Parameters

  1. Element(questionList, questionListIndex) → questionNum
  2. UnicodeToLetter(10003) → cmark
  3. UnicodeToLetter(10007) → xmark
  4. Element(B2:B7, questionNum) → correctRightText
  5. Element(C2:C7, questionNum) → correctLeftText
  6. Element(D2:D7, questionNum) → incorrectRightText
  7. Element(E2:E7, questionNum) → incorrectLeftText
  8. Element(F2:F7, questionNum) → feedback
  9. Element(A2:A7, questionNum) → questionText
  10. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  11. LaTeX("t \ne 0, 2") → B2
  12. LaTeX("\dfrac{3}{4t^2}") → C2
  13. LaTeX("\dfrac{3(t-2)}{2t(2t^2-4t)}") → E2
  14. LaTeX("x \ne -3") → B4
  15. LaTeX("x \ne 3") → D4
  16. LaTeX("x-3") → C4
  17. LaTeX("\dfrac{x^2-9}{x+3}") → E4
  18. LaTeX("x \ne -1, -3") → B5
  19. LaTeX("\dfrac{x+1}{x+3}") → C5
  20. LaTeX("\dfrac{2x+1}{4x+3}") → E5
  21. LaTeX("t \ne 1, -\tfrac{1}{2}") → B6
  22. LaTeX("\dfrac{t^2}{t-1}") → C6
  23. LaTeX("\dfrac{t^2}{t+1}") → E6
  24. LaTeX("\dfrac{(t\hspace{-4}-\hspace{-4}1)(t\hspace{-4}+\hspace{-4}5)}{(t\hspace{-4}-\hspace{-4}5)(1\hspace{-4}-\hspace{-4}t)}") → A3
  25. LaTeX("t \ne 1, 5") → B3
  26. LaTeX("-\dfrac{t+5}{t-5}") → C3
  27. LaTeX("\dfrac{t+5}{t-5}") → E3
  28. LaTeX("\dfrac{3t-6}{4t^3-8t^2}") → A2
  29. LaTeX("\dfrac{2x^2-18}{2x+6}") → A4
  30. LaTeX("\dfrac{x^2+2x+1}{x^2+4x+3}") → A5
  31. LaTeX("\dfrac{6t^3+3t^2}{6t^2-3t-3}") → A6
  32. Text(If[isRightCorrect, correctRightText, incorrectRightText], puzzleAnchor + (9.5, 7.5), true, true) → matchedRightText
  33. Text(If[isLeftCorrect, correctLeftText, incorrectLeftText], puzzleAnchor + (2.75, 5.25), true, true) → matchedLeftText
  34. LaTeX("t \ne 0") → D2
  35. LaTeX("t \ne 5") → D3
  36. LaTeX("x \ne -3") → D5
  37. LaTeX("t \ne 1") → D6

AI Drawing Prompt Reference

Draw the simplified forms of the following rational expressions and their domain restrictions: 1. 3/(4t^2), t ≠ 0, 2; 2. (3(t-2))/(2t(2t^2-4t)), t ≠ 0, 2; 3. (x^2-9)/(x+3), x ≠ -3; 4. (t^2)/(t-1), t ≠ 1, -1/2; 5. (t^2)/(t+1), t ≠ -1, -3; 6. ((t-1)(t+5))/((t-5)(1-t)), t ≠ 1, 5; 7. (3t-6)/(4t^3-8t^2), t ≠ 0; 8. (2x^2-18)/(2x+6), x ≠ -3; 9. (x^2+2x+1)/(x^2+4x+3), x ≠ -3; 10. (6t^3+3t^2)/(6t^2-3t-3), t ≠ 1, -1/2.
The prompt above was compiled from the original drawing commands and is for reference only.