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Grade 10 · Algebraic Expressions
Algebraic Fractions: Simplify, Add & Subtract (Grade 10)
MEMORANDUM
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  / 23

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

  1. 1
    Simplify: (x2 − 16)/(x + 4)
    (2)
    x − 4,  x ≠ −4✓✓ (2)
  2. 2
    Simplify: (x2 − 25)/(x − 5)
    (2)
    x + 5,  x ≠ 5✓✓ (2)
  3. 3
    Simplify: (x2 + 5x + 6)/(x2 − 4)
    (3)
    (x + 3)/(x − 2),  x ≠ ±2✓✓✓ (3)
  4. 4
    Simplify: 6x2/3x
    (1)
    2x,  x ≠ 0✓ (1)
  5. 5
    Simplify: (x2 − 1)/x ÷ (x + 1)/3x
    (4)
    3(x − 1),  x ≠ 0, x ≠ −1✓✓✓✓ (4)
  6. 6
    Simplify: 1/x + 1/y
    (2)
    (y + x)/xy,  x ≠ 0, y ≠ 0✓✓ (2)
  7. 7
    Simplify: 2/(x + 1) + 3/(x − 1)
    (3)
    (5x + 1)/(x2 − 1),  x ≠ ±1✓✓✓ (3)
  8. 8
    Simplify: (x − 2)/(x3 − 8)
    (3)
    1/(x2 + 2x + 4),  x ≠ 2✓✓✓ (3)
  9. 9
    Simplify: (x + 3)/(x3 + 27)
    (3)
    1/(x2 − 3x + 9),  x ≠ −3✓✓✓ (3)
TOTAL: 23 marks
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