Back to Common Core worksheets
PrintablePractice worksheetRiddle puzzleFlashcardsBingo game
Do it🖨️ On paper✏️ On screen
Layout1 column2 columns
Answer keyNoneAnswersWith steps
Questions10162430
LevelEasierMixedHarder
Print sizeNormalLarge print
New copyMake a new one

Free to print and copy for home or class. This link always prints the same sheet.

eurekami

Common Core HSA.APR.D.7 worksheet

High school · 16 questions · Common Core: HSA.APR.D.6, HSA.APR.D.7 · England: GCSE Higher Algebra

Name

Date

Score/ 16

  1. Question 1

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

    Answer

  2. Question 2

    Simplify: (x² − 1)/x ÷ (x − 1)/(2x²)

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

  3. Question 3

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

    • A. 2/(x + 2)
    • B. 1/(x + 2)
    • C. 2/(x² − 4)
    • D. (x − 3)/(x² − 4)

  4. Question 4

    Simplify: (x² − 5x − 14) / (x + 2)

    • A. x + 7
    • B. x + 2
    • C. x − 14
    • D. x − 7

  5. Question 5

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

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

  6. Question 6

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

    • A. (x + 9)/((x + 4)(x + 5))
    • B. 1/((x + 4)(x + 5))
    • C. (x + 41)/((x + 4)(x + 5))
    • D. (x + 9)/((x + 4) + (x + 5))

  7. Question 7

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

    Answer

  8. Question 8

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

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

  9. Question 9

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

    • A. 6/(x + 2)
    • B. (x − 8)/(x² − 4)
    • C. 7/(x + 2)
    • D. 7/(x − 2)

  10. Question 10

    Simplify: (x² + 5x − 14) / (x + 7)

    • A. x + 7
    • B. x + 2
    • C. x − 14
    • D. x − 2

  11. Question 11

    Simplify: (x² − 36)/(x − 6) × (x − 6)/(x − 6)

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

  12. Question 12

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

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

  13. Question 13

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

    Answer

  14. Question 14

    Simplify: (x² − 5x − 6)/x ÷ (x + 1)/(5x²)

    • A. 5x²(x − 6)
    • B. 5x(x + 1)
    • C. 5(x − 6)
    • D. 5x(x − 6)

  15. Question 15

    Simplify: 3/(x + 4) + (x − 4)/(x² − 16)

    • A. 4/(x² − 16)
    • B. (x − 7)/(x² − 16)
    • C. 3/(x + 4)
    • D. 4/(x + 4)

  16. Question 16

    Simplify: (x² − 7x + 10) / (x − 2)

    • A. x + 10
    • B. x + 5
    • C. x − 5
    • D. x − 2

All done? Color in the animal! · Free from eurekami.com/math

for the adult only

Answer key: Common Core HSA.APR.D.7 worksheet

  1. 1. (10x+35)/((x+4)(x+3))

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

  3. 3. A. 2/(x + 2)

  4. 4. D. x − 7

  5. 5. B. (x + 4)

  6. 6. A. (x + 9)/((x + 4)(x + 5))

  7. 7. (5x+22)/((x+2)(x+5))

  8. 8. D. 2x(x − 2)

  9. 9. C. 7/(x + 2)

  10. 10. D. x − 2

  11. 11. C. (x + 6)

  12. 12. C. (7x − 1)/((x + 1)(x − 1))

  13. 13. (4x+5)/((x+1)(x+2))

  14. 14. D. 5x(x − 6)

  15. 15. D. 4/(x + 4)

  16. 16. C. x − 5

HSA.APR.D.7 Worksheet: Algebraic fractions | Eurekami