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Algebraic fractions

10th grade (Year 11 in England) · 16 questions · Common Core: HSA.APR.D.6, HSA.APR.D.7 · England: GCSE Higher Algebra

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Score/ 16

  1. Question 1

    Write as a single fraction: 3/(x + 5) + 1/(x + 1). Type the numerator over the factorised denominator, e.g. (3x+5)/((x+1)(x+2)).

    Answer

  2. Question 2

    Simplify: (x² + 3x + 2) / (x + 1)

    • A. x − 2
    • B. x + 2
    • C. x + 1
    • D. x + 3

  3. Question 3

    Write as a single fraction: 4/(x + 6) + 5/(x + 5). Type the numerator over the factorised denominator, e.g. (3x+5)/((x+1)(x+2)).

    Answer

  4. Question 4

    Simplify: (x² + 5x + 4) / (x + 4)

    • A. x + 5
    • B. x − 1
    • C. x + 4
    • D. x + 1

  5. Question 5

    Write as a single fraction: 2/(x + 4) + 3/(x + 3). Type the numerator over the factorised denominator, e.g. (3x+5)/((x+1)(x+2)).

    Answer

  6. Question 6

    Simplify: (x² + 3x − 4) / (x − 1)

    • A. x − 4
    • B. x + 3
    • C. x − 1
    • D. x + 4

  7. Question 7

    Write as a single fraction: 5/(x + 3) + 5/(x + 2). Type the numerator over the factorised denominator, e.g. (3x+5)/((x+1)(x+2)).

    Answer

  8. Question 8

    Simplify: (x² − 49) / (x + 7)

    • A. x − 7
    • B. x
    • C. x − 49
    • D. x + 7

  9. Question 9

    Write as a single fraction: 1/(x + 4) + 3/(x + 1). Type the numerator over the factorised denominator, e.g. (3x+5)/((x+1)(x+2)).

    Answer

  10. Question 10

    Simplify: (x² − 3x + 2) / (x − 1)

    • A. x − 3
    • B. x − 2
    • C. x − 1
    • D. x + 2

  11. Question 11

    Write as a single fraction: 5/(x + 3) + 4/(x + 2). Type the numerator over the factorised denominator, e.g. (3x+5)/((x+1)(x+2)).

    Answer

  12. Question 12

    Simplify: (x² − x − 12) / (x + 3)

    • A. x − 12
    • B. x − 4
    • C. x − 1
    • D. x + 3

  13. Question 13

    Write as a single fraction: 4/(x + 3) + 3/(x + 6). Type the numerator over the factorised denominator, e.g. (3x+5)/((x+1)(x+2)).

    Answer

  14. Question 14

    Simplify: (x² − 3x − 4) / (x + 1)

    • A. x + 1
    • B. x − 3
    • C. x − 4
    • D. x + 4

  15. Question 15

    Write as a single fraction: 5/(x + 6) + 2/(x + 3). Type the numerator over the factorised denominator, e.g. (3x+5)/((x+1)(x+2)).

    Answer

  16. Question 16

    Simplify: (x² − 16) / (x + 4)

    • A. x − 4
    • B. x − 16
    • C. x + 4
    • D. x

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Answer key: Algebraic fractions

  1. 1. (4x+8)/((x+5)(x+1))

  2. 2. B. x + 2

  3. 3. (9x+50)/((x+6)(x+5))

  4. 4. D. x + 1

  5. 5. (5x+18)/((x+4)(x+3))

  6. 6. D. x + 4

  7. 7. (10x+25)/((x+3)(x+2))

  8. 8. A. x − 7

  9. 9. (4x+13)/((x+4)(x+1))

  10. 10. B. x − 2

  11. 11. (9x+22)/((x+3)(x+2))

  12. 12. B. x − 4

  13. 13. (7x+33)/((x+3)(x+6))

  14. 14. C. x − 4

  15. 15. (7x+27)/((x+6)(x+3))

  16. 16. A. x − 4