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Simplify algebraic fractions by factorising

10th grade (Year 11 in England) · 16 questions · Common Core: HSA.APR.D.6, HSA.SSE.A.2 · England: GCSE Higher Algebra

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Score/ 16

1
Question 1
Sofia simplified (x + 8)/x by crossing out the x's and got 1 + 8 = 9. Is this right?
- A. Right
- B. Wrong: only common factors can be cancelled, not terms
- C. Right, but only when x is positive
2
Question 2
Simplify: (x² − x − 30)/(x − 6)
- A. (x − 1)
- B. (x − 5)
- C. (x − 30)
- D. (x + 5)
3
Question 3
Chloe simplified (x + 6)/x by crossing out the x's and got 1 + 6 = 7. Is this right?
- A. Right
- B. Wrong: only common factors can be cancelled, not terms
- C. Right, but only when x is positive
4
Question 4
Simplify: (x² − 4)/(x + 2)
- A. (x − 2)
- B. 1/(x − 2)
- C. x − 4
- D. (x² − 2)
5
Question 5
Leo simplified (x + 3)/x by crossing out the x's and got 1 + 3 = 4. Is this right?
- A. Right
- B. Wrong: only common factors can be cancelled, not terms
- C. Right, but only when x is positive
6
Question 6
Simplify: (x² + 4x + 3)/(x + 1)
- A. (x + 3)/(x + 1)
- B. (x + 3)
- C. (x + 4)
- D. (x − 3)
7
Question 7
Maya simplified (x + 6)/x by crossing out the x's and got 1 + 6 = 7. Is this right?
- A. Right
- B. Wrong: only common factors can be cancelled, not terms
- C. Right, but only when x is positive
8
Question 8
Simplify: (x² − 3x − 4)/(x² − 16)
- A. (x + 1)/(x + 4)
- B. (x − 1)/(x + 4)
- C. (x + 1)/(x − 4)
- D. (x − 4)/(x + 4)
9
Question 9
Daniel simplified (x + 2)/x by crossing out the x's and got 1 + 2 = 3. Is this right?
- A. Right
- B. Wrong: only common factors can be cancelled, not terms
- C. Right, but only when x is positive
10
Question 10
Simplify: (x² + 7x + 6)/(x² − 36)
- A. (x + 1)/(x + 6)
- B. (x + 7)/(x − 36)
- C. (x + 1)/(x − 6)
- D. (x − 1)/(x − 6)
11
Question 11
Aisha simplified (x + 4)/x by crossing out the x's and got 1 + 4 = 5. Is this right?
- A. Right
- B. Wrong: only common factors can be cancelled, not terms
- C. Right, but only when x is positive
12
Question 12
Simplify: (x² + 14x + 48)/(x + 6)
- A. (x + 8)/(x + 6)
- B. (x + 8)
- C. (x + 48)
- D. (x + 14)
13
Question 13
Kwame simplified (x + 4)/x by crossing out the x's and got 1 + 4 = 5. Is this right?
- A. Right
- B. Wrong: only common factors can be cancelled, not terms
- C. Right, but only when x is positive
14
Question 14
Simplify: (x² + 5x − 14)/(x² − 49)
- A. (x + 5)/(x − 49)
- B. (x + 2)/(x − 7)
- C. (x − 2)/(x − 7)
- D. (x − 2)/(x + 7)
15
Question 15
Kai simplified (x + 5)/x by crossing out the x's and got 1 + 5 = 6. Is this right?
- A. Right
- B. Wrong: only common factors can be cancelled, not terms
- C. Right, but only when x is positive
16
Question 16
Simplify: (x² − 4)/(x + 2)
- A. (x − 2)
- B. (x² − 2)
- C. x − 4
- D. 1/(x − 2)

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