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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

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

    • A. (5x − 19)/((x + 5)(x − 2))
    • B. (5x + 11)/((x + 5)(x − 2))
    • C. (5x + 11)/((x + 5) + (x − 2))
    • D. 5/((x + 5)(x − 2))

  2. Question 2

    Simplify: 3/(x + 6) + (x − 6)/(x² − 36)

    • A. 3/(x + 6)
    • B. 4/(x² − 36)
    • C. (x − 9)/(x² − 36)
    • D. 4/(x + 6)

  3. Question 3

    Write as a single fraction: 2/(x + 3) + 2/(x + 4)

    • A. 4/((x + 3)(x + 4))
    • B. (4x + 14)/((x + 3) + (x + 4))
    • C. (4x + 2)/((x + 3)(x + 4))
    • D. (4x + 14)/((x + 3)(x + 4))

  4. Question 4

    Simplify: 2/(x + 4) + (x − 4)/(x² − 16)

    • A. (x − 6)/(x² − 16)
    • B. 3/(x + 4)
    • C. 2/(x + 4)
    • D. 3/(x − 4)

  5. Question 5

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

    • A. (−2x − 2)/((x − 1) + (x − 5))
    • B. (−2x − 8)/((x − 1)(x − 5))
    • C. -2/((x − 1)(x − 5))
    • D. (−2x − 2)/((x − 1)(x − 5))

  6. Question 6

    Simplify: 2/(x + 6) + (x − 6)/(x² − 36)

    • A. 2/(x + 6)
    • B. (x − 8)/(x² − 36)
    • C. 3/(x + 6)
    • D. 3/(x² − 36)

  7. Question 7

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

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

  8. Question 8

    Simplify: 6/(x + 4) + (x − 4)/(x² − 16)

    • A. 7/(x − 4)
    • B. (x − 10)/(x² − 16)
    • C. 6/(x + 4)
    • D. 7/(x + 4)

  9. Question 9

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

    • A. (7x − 21)/((x + 3)(x − 3))
    • B. (7x − 9)/((x + 3)(x − 3))
    • C. 7/((x + 3)(x − 3))
    • D. (7x − 9)/((x + 3) + (x − 3))

  10. Question 10

    Simplify: 1/(x + 2) + (x − 2)/(x² − 4)

    • A. (x − 3)/(x² − 4)
    • B. 2/(x² − 4)
    • C. 2/(x + 2)
    • D. 2/(x − 2)

  11. Question 11

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

    • A. (7x + 27)/((x − 3)(x + 6))
    • B. (7x − 3)/((x − 3)(x + 6))
    • C. 7/((x − 3)(x + 6))
    • D. (7x − 3)/((x − 3) + (x + 6))

  12. Question 12

    Simplify: 2/(x + 6) + (x − 6)/(x² − 36)

    • A. 2/(x + 6)
    • B. 3/(x² − 36)
    • C. 3/(x + 6)
    • D. (x − 8)/(x² − 36)

  13. Question 13

    Write as a single fraction: 4/(x + 3) − 2/(x + 5)

    • A. (2x + 14)/((x + 3)(x + 5))
    • B. 2/((x + 3)(x + 5))
    • C. (2x + 14)/((x + 3) + (x + 5))
    • D. (2x + 26)/((x + 3)(x + 5))

  14. Question 14

    Simplify: 4/(x + 5) + (x − 5)/(x² − 25)

    • A. (x − 9)/(x² − 25)
    • B. 5/(x + 5)
    • C. 5/(x − 5)
    • D. 5/(x² − 25)

  15. Question 15

    Write as a single fraction: 3/(x − 4) + 4/(x + 2)

    • A. 7/((x − 4)(x + 2))
    • B. (7x − 10)/((x − 4)(x + 2))
    • C. (7x − 10)/((x − 4) + (x + 2))
    • D. (7x + 22)/((x − 4)(x + 2))

  16. Question 16

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

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

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Answer key: Add and subtract algebraic fractions

  1. 1. B. (5x + 11)/((x + 5)(x − 2))

  2. 2. D. 4/(x + 6)

  3. 3. D. (4x + 14)/((x + 3)(x + 4))

  4. 4. B. 3/(x + 4)

  5. 5. D. (−2x − 2)/((x − 1)(x − 5))

  6. 6. C. 3/(x + 6)

  7. 7. D. (2x)/((x − 4)(x + 4))

  8. 8. D. 7/(x + 4)

  9. 9. B. (7x − 9)/((x + 3)(x − 3))

  10. 10. C. 2/(x + 2)

  11. 11. B. (7x − 3)/((x − 3)(x + 6))

  12. 12. C. 3/(x + 6)

  13. 13. A. (2x + 14)/((x + 3)(x + 5))

  14. 14. B. 5/(x + 5)

  15. 15. B. (7x − 10)/((x − 4)(x + 2))

  16. 16. D. 5/(x + 4)