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Add and subtract algebraic fractions

11th grade (Year 12 in England) · 16 questions · Common Core: HSA.APR.D.7 · England: GCSE Higher Algebra

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  1. Question 1

    Simplify: 4/(x + 7) + (x − 7)/(x² − 49)

    • A. 5/(x + 7)
    • B. 4/(x + 7)
    • C. 5/(x − 7)
    • D. (x − 11)/(x² − 49)

  2. Question 2

    Write as a single fraction: 2/(x − 6) + 1/(x − 3)

    • A. (3x)/((x − 6)(x − 3))
    • B. (3x − 12)/((x − 6) + (x − 3))
    • C. (3x − 12)/((x − 6)(x − 3))
    • D. 3/((x − 6)(x − 3))

  3. Question 3

    Simplify: 6/(x + 3) + (x − 3)/(x² − 9)

    • A. 7/(x + 3)
    • B. 7/(x² − 9)
    • C. 7/(x − 3)
    • D. (x − 9)/(x² − 9)

  4. Question 4

    Write as a single fraction: 3/(x − 6) + 2/(x − 5)

    • A. 5/((x − 6)(x − 5))
    • B. (5x − 3)/((x − 6)(x − 5))
    • C. (5x − 27)/((x − 6) + (x − 5))
    • D. (5x − 27)/((x − 6)(x − 5))

  5. Question 5

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

    • A. 6/(x² − 9)
    • B. 6/(x − 3)
    • C. 6/(x + 3)
    • D. (x − 8)/(x² − 9)

  6. Question 6

    Write as a single fraction: 2/(x + 1) − 3/(x + 3)

    • A. (−x + 9)/((x + 1)(x + 3))
    • B. (−x + 3)/((x + 1)(x + 3))
    • C. -1/((x + 1)(x + 3))
    • D. (−x + 3)/((x + 1) + (x + 3))

  7. Question 7

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

    • A. (x − 5)/(x² − 9)
    • B. 2/(x + 3)
    • C. 3/(x − 3)
    • D. 3/(x + 3)

  8. Question 8

    Write as a single fraction: 5/(x − 3) + 1/(x − 2)

    • A. (6x − 13)/((x − 3)(x − 2))
    • B. (6x − 7)/((x − 3)(x − 2))
    • C. 6/((x − 3)(x − 2))
    • D. (6x − 13)/((x − 3) + (x − 2))

  9. Question 9

    Simplify: 6/(x + 7) + (x − 7)/(x² − 49)

    • A. 7/(x − 7)
    • B. (x − 13)/(x² − 49)
    • C. 6/(x + 7)
    • D. 7/(x + 7)

  10. Question 10

    Write as a single fraction: 2/(x + 6) + 3/(x + 3)

    • A. 5/((x + 6)(x + 3))
    • B. (5x − 12)/((x + 6)(x + 3))
    • C. (5x + 24)/((x + 6)(x + 3))
    • D. (5x + 24)/((x + 6) + (x + 3))

  11. Question 11

    Simplify: 6/(x + 5) + (x − 5)/(x² − 25)

    • A. 6/(x + 5)
    • B. 7/(x² − 25)
    • C. (x − 11)/(x² − 25)
    • D. 7/(x + 5)

  12. Question 12

    Write as a single fraction: 4/(x − 3) + 1/(x + 4)

    • A. (5x + 19)/((x − 3)(x + 4))
    • B. 5/((x − 3)(x + 4))
    • C. (5x + 13)/((x − 3) + (x + 4))
    • D. (5x + 13)/((x − 3)(x + 4))

  13. Question 13

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

    • A. 5/(x + 4)
    • B. 4/(x + 4)
    • C. (x − 8)/(x² − 16)
    • D. 5/(x − 4)

  14. Question 14

    Write as a single fraction: 5/(x + 6) − 2/(x − 1)

    • A. 3/((x + 6)(x − 1))
    • B. (3x − 17)/((x + 6)(x − 1))
    • C. (3x + 7)/((x + 6)(x − 1))
    • D. (3x − 17)/((x + 6) + (x − 1))

  15. Question 15

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

    • A. 5/(x² − 16)
    • B. 5/(x − 4)
    • C. 5/(x + 4)
    • D. (x − 8)/(x² − 16)

  16. Question 16

    Write as a single fraction: 4/(x − 4) + 4/(x − 2)

    • A. 8/((x − 4)(x − 2))
    • B. (8x + 8)/((x − 4)(x − 2))
    • C. (8x − 24)/((x − 4) + (x − 2))
    • D. (8x − 24)/((x − 4)(x − 2))

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  1. 5/(x + 7)
  2. (3x − 12)/((x − 6)(x − 3))
  3. 7/(x + 3)
  4. (5x − 27)/((x − 6)(x − 5))
  5. 6/(x + 3)
  6. (−x + 3)/((x + 1)(x + 3))
  7. 3/(x + 3)
  8. (6x − 13)/((x − 3)(x − 2))
  9. 7/(x + 7)
  10. (5x + 24)/((x + 6)(x + 3))
  11. 7/(x + 5)
  12. (5x + 13)/((x − 3)(x + 4))
  13. 5/(x + 4)
  14. (3x − 17)/((x + 6)(x − 1))
  15. 5/(x + 4)
  16. (8x − 24)/((x − 4)(x − 2))