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Junior Cycle · Junior Cycle Maths

Junior Cycle Maths: Algebraic fractions

How often Algebraic fractions comes up on the Maths papers, every year it was asked, and questions to try.

HL Asked on 3 of the last 5 Higher Level papers, most recently in 2026. most years

Algebraic fractions, Higher Level(9 marks)

Quick ones on Algebraic fractions.

(a)Write (x + 1)/2 + (x − 3)/5 as a single fraction.
  1. (2x − 2)/7
  2. (7x − 1)/10
  3. (7x + 11)/10
(b)Write 2/(x + 1) + 3/(x − 2) as a single fraction.
  1. (5x + 7)/((x + 1)(x − 2))
  2. 5/(2x − 1)
  3. (5x − 1)/((x + 1)(x − 2))
(c)Write 3/(x − 1) − 2/x as a single fraction.
  1. (x + 2)/(x(x − 1))
  2. 1/(x(x − 1))
  3. (x − 2)/(x(x − 1))
Show the answers

(a) (7x − 1)/10

(b) (5x − 1)/((x + 1)(x − 2))

(c) (x + 2)/(x(x − 1))

Your turn: Higher Level questions on Algebraic fractions.

Higher Level

Asked on 3 of the last 5 Higher Level papers, most recently in 2026. most years

Every paper, year by year

YearWhere it came up
2026Q9
2025Not asked
2024Q11
2023Not asked
2022Q9

Links open the State Examinations Commission’s paper for that year.

More Algebraic fractions questions

Algebraic fractions, 3 marks

Solve 2/(x + 1) = 3/(x − 1).

  1. x = 5
  2. x = −1/5
  3. x = −5
Show the answer

x = −5

Cross-multiply: 2(x − 1) = 3(x + 1), so 2x − 2 = 3x + 3 and x = −5. Check: 2/(−4) = −0.5 and 3/(−6) = −0.5.

Algebraic fractions, 2 marks

Simplify (x² − 9)/(x + 3).

  1. x² − 3
  2. x − 3
  3. x + 3
Show the answer

x − 3

Factorise the top as a difference of two squares: (x − 3)(x + 3). Cancel the common factor (x + 3) to leave x − 3.

Other Maths topics

All of Junior Cycle Maths