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Multiply and divide algebraic fractions

10th grade (Year 11 in England) · 16 questions · Common Core: HSA.APR.D.7 · England: GCSE Higher Algebra

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  1. Question 1

    Simplify: (x² + 7x + 10)/x ÷ (x + 2)/(3x²)

    • A. (x + 5)/(3x)
    • B. 3x²(x + 5)
    • C. 3x(x + 5)
    • D. 3x(x + 2)

  2. Question 2

    Simplify: (x² − 1)/(x + 6) × (x + 6)/(x − 1)

    • A. (x − 1)
    • B. 1
    • C. (x + 1)
    • D. (x + 1)/(x + 6)

  3. Question 3

    Simplify: (x² − 16)/x ÷ (x + 4)/(5x²)

    • A. 5(x − 4)
    • B. (x − 4)/(5x)
    • C. 5x(x + 4)
    • D. 5x(x − 4)

  4. Question 4

    Simplify: (x² − 16)/(x − 4) × (x − 4)/(x − 4)

    • A. 1
    • B. x² − 16
    • C. (x + 4)/(x − 4)
    • D. (x + 4)

  5. Question 5

    Simplify: (x² + 7x + 12)/x ÷ (x + 3)/(2x²)

    • A. 2x(x + 3)
    • B. 2x(x + 4)
    • C. 2(x + 4)
    • D. (x + 4)/(2x)

  6. Question 6

    Simplify: (x² − 25)/(x − 3) × (x − 3)/(x − 5)

    • A. (x + 5)
    • B. (x + 5)/(x − 3)
    • C. 1
    • D. (x − 5)

  7. Question 7

    Simplify: (x² − 11x + 30)/x ÷ (x − 5)/(3x²)

    • A. 3x²(x − 6)
    • B. 3x(x − 6)
    • C. 3(x − 6)
    • D. (x − 6)/(3x)

  8. Question 8

    Simplify: (x² − 4)/(x − 6) × (x − 6)/(x − 2)

    • A. (x + 2)/(x − 6)
    • B. x² − 4
    • C. 1
    • D. (x + 2)

  9. Question 9

    Simplify: (x² + 4x + 3)/x ÷ (x + 3)/(2x²)

    • A. 2(x + 1)
    • B. (x + 1)/(2x)
    • C. 2x(x + 1)
    • D. 2x²(x + 1)

  10. Question 10

    Simplify: (x² − 49)/(x + 5) × (x + 5)/(x − 7)

    • A. (x + 7)
    • B. 1
    • C. (x − 7)
    • D. (x + 7)/(x + 5)

  11. Question 11

    Simplify: (x² + x − 20)/x ÷ (x + 5)/(4x²)

    • A. 4x(x + 5)
    • B. 4x²(x − 4)
    • C. 4(x − 4)
    • D. 4x(x − 4)

  12. Question 12

    Simplify: (x² − 64)/(x − 6) × (x − 6)/(x − 8)

    • A. (x − 8)
    • B. (x + 8)
    • C. (x + 8)/(x − 6)
    • D. x² − 64

  13. Question 13

    Simplify: (x² − 2x − 15)/x ÷ (x − 5)/(3x²)

    • A. 3x²(x + 3)
    • B. 3x(x + 3)
    • C. 3x(x − 5)
    • D. (x + 3)/(3x)

  14. Question 14

    Simplify: (x² − 9)/(x − 2) × (x − 2)/(x − 3)

    • A. (x + 3)/(x − 2)
    • B. (x + 3)
    • C. x² − 9
    • D. (x − 3)

  15. Question 15

    Simplify: (x² − 9)/x ÷ (x + 3)/(5x²)

    • A. 5(x − 3)
    • B. 5x²(x − 3)
    • C. 5x(x − 3)
    • D. 5x(x + 3)

  16. Question 16

    Simplify: (x² − 4)/(x − 2) × (x − 2)/(x − 2)

    • A. (x − 2)
    • B. 1
    • C. (x + 2)
    • D. (x + 2)/(x − 2)

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Answer key: Multiply and divide algebraic fractions

  1. 1. C. 3x(x + 5)

  2. 2. C. (x + 1)

  3. 3. D. 5x(x − 4)

  4. 4. D. (x + 4)

  5. 5. B. 2x(x + 4)

  6. 6. A. (x + 5)

  7. 7. B. 3x(x − 6)

  8. 8. D. (x + 2)

  9. 9. C. 2x(x + 1)

  10. 10. A. (x + 7)

  11. 11. D. 4x(x − 4)

  12. 12. B. (x + 8)

  13. 13. B. 3x(x + 3)

  14. 14. B. (x + 3)

  15. 15. C. 5x(x − 3)

  16. 16. C. (x + 2)