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Grade 11 · Practice problems

Simplifying

50 written problems across two levels — 32 foundational · 18 advanced. Work through them on paper, then reveal every answer to check. These are not graded and are counted separately from adaptive practice.

    Foundational

  1. 1. FoundationalState the restriction on 5x−2\dfrac{5}{x - 2}.

  2. 2. FoundationalState the restriction on x+1x\dfrac{x + 1}{x}.

  3. 3. FoundationalSimplify 6x3x\dfrac{6x}{3x}.

  4. 4. FoundationalSimplify 2x4x2\dfrac{2x}{4x^2}.

  5. 5. FoundationalState the restrictions on 3(x−1)(x+4)\dfrac{3}{(x - 1)(x + 4)}.

  6. 6. FoundationalSimplify x2x\dfrac{x^2}{x}.

  7. 7. FoundationalReduce 1218\dfrac{12}{18}.

  8. 8. FoundationalSimplify 5x210x\dfrac{5x^2}{10x}.

  9. 9. FoundationalState the restrictions on xx2−9\dfrac{x}{x^2 - 9}.

  10. 10. FoundationalSimplify 4a2a\dfrac{4a}{2a}.

  11. 11. FoundationalSimplify x2−9x+3\dfrac{x^2 - 9}{x + 3}.

  12. 12. FoundationalSimplify x2−4x−2\dfrac{x^2 - 4}{x - 2}.

  13. 13. FoundationalSimplify 2x+6x2−9\dfrac{2x + 6}{x^2 - 9}.

  14. 14. FoundationalSimplify x2−x−6x2−4\dfrac{x^2 - x - 6}{x^2 - 4}.

  15. 15. FoundationalSimplify x2+5x+6x+2\dfrac{x^2 + 5x + 6}{x + 2}.

  16. 16. FoundationalSimplify 3x−12x−4\dfrac{3x - 12}{x - 4}.

  17. 17. FoundationalSimplify x2−16x2+4x\dfrac{x^2 - 16}{x^2 + 4x}.

  18. 18. FoundationalSimplify x2−25x2−5x\dfrac{x^2 - 25}{x^2 - 5x}.

  19. 19. FoundationalState the restrictions on x+2x2−x−6\dfrac{x + 2}{x^2 - x - 6}.

  20. 20. FoundationalSimplify 6x29x3\dfrac{6x^2}{9x^3}.

  21. 21. FoundationalSimplify x2−1x2+2x+1\dfrac{x^2 - 1}{x^2 + 2x + 1}.

  22. 22. FoundationalSimplify 2x2+8xx2+4x\dfrac{2x^2 + 8x}{x^2 + 4x}.

  23. 23. FoundationalSimplify x2−7x+12x−3\dfrac{x^2 - 7x + 12}{x - 3}.

  24. 24. FoundationalSimplify x2+6x+9x+3\dfrac{x^2 + 6x + 9}{x + 3}.

  25. 25. FoundationalState the restrictions on 7x2+1\dfrac{7}{x^2 + 1}.

  26. 26. FoundationalSimplify 5x−102x−4\dfrac{5x - 10}{2x - 4}.

  27. 27. FoundationalSimplify x2−4xx2−16\dfrac{x^2 - 4x}{x^2 - 16}.

  28. 28. FoundationalSimplify x3x2\dfrac{x^3}{x^2}.

  29. 29. FoundationalSimplify a2−b2a−b\dfrac{a^2 - b^2}{a - b}.

  30. 30. FoundationalSimplify x2−9x+20x2−25\dfrac{x^2 - 9x + 20}{x^2 - 25}.

  31. 31. FoundationalSimplify 4−x2x−2\dfrac{4 - x^2}{x - 2}.

  32. 32. FoundationalState the restrictions on 2x−1(x−5)(2x+3)\dfrac{2x - 1}{(x - 5)(2x + 3)}.

    33. Advanced

  33. 33. AdvancedSimplify 3−xx2−9\dfrac{3 - x}{x^2 - 9}.

  34. 34. AdvancedSimplify x2−5x+66−x−x2\dfrac{x^2 - 5x + 6}{6 - x - x^2}.

  35. 35. AdvancedSimplify 2x2−8x2−x−2\dfrac{2x^2 - 8}{x^2 - x - 2}.

  36. 36. AdvancedSimplify x2−92x2+5x−3\dfrac{x^2 - 9}{2x^2 + 5x - 3}.

  37. 37. AdvancedSimplify a−bb−a\dfrac{a - b}{b - a}.

  38. 38. AdvancedSimplify (x+2)2x2−4\dfrac{(x + 2)^2}{x^2 - 4}.

  39. 39. AdvancedSimplify x3−xx2−1\dfrac{x^3 - x}{x^2 - 1}.

  40. 40. AdvancedSimplify 6x2+x−24x2−1\dfrac{6x^2 + x - 2}{4x^2 - 1}.

  41. 41. AdvancedSimplify x2−4x2+4x+4\dfrac{x^2 - 4}{x^2 + 4x + 4}.

  42. 42. AdvancedSimplify x2−1x2−x−2\dfrac{x^2 - 1}{x^2 - x - 2} and state all restrictions.

  43. 43. AdvancedSimplify x2+x−12x2−9\dfrac{x^2 + x - 12}{x^2 - 9}.

  44. 44. AdvancedSimplify 10−2xx2−25\dfrac{10 - 2x}{x^2 - 25}.

  45. 45. AdvancedSimplify x2−6x+9x2−9\dfrac{x^2 - 6x + 9}{x^2 - 9}.

  46. 46. AdvancedA rectangle's area is x2+7x+12x^2 + 7x + 12 and its width is x+3x + 3. Find its length.

  47. 47. AdvancedSimplify x4−16x2−4\dfrac{x^4 - 16}{x^2 - 4}.

  48. 48. AdvancedSimplify 3x2−129x−18\dfrac{3x^2 - 12}{9x - 18}.

  49. 49. AdvancedExplain why x+5x+3\dfrac{x + 5}{x + 3} cannot be simplified by cancelling the xx's.

  50. 50. AdvancedSimplify x2−9x3+27\dfrac{x^2 - 9}{x^3 + 27}.