Robinson Tuition
Grade 8 · Higher · free GCSE maths worksheet

Algebraic fractions: adding, subtracting and solving

Equations with algebraic denominators.

11 original questions, 43 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Write x + 12 + 2x − 15 as a single fraction in its simplest form.

2 marks
Show answer
(9x + 3)/10
2

Write 3x + 1 − 2x + 4 as a single fraction. Simplify the numerator.

3 marks
Show answer
(x + 10)/((x + 1)(x + 4))
3

Show that

4x + 3 − 2x + 5

can be written as 2(x + 7)(x + 3)(x + 5)

3 marks
Show answer
2(x+7)(x+3)(x+5)
4

Solve

x + 43 + 2x − 15 = 7

3 marks
Show answer
x = 8
5

Solve

4x − 1 − 2x + 2 = 1

4 marks
Show answer
x = 4 or x = -3
6

Solve

1x − 2 + 2x + 1 = 3

Give your answers in the form a ± √b where a and b are integers.

5 marks
Show answer
x = 1 + sqrt(2) or x = 1 - sqrt(2)
7

Show that

x2 + 3xx2 − x − 12 − 2x + 1

can be written as x2 − x + 8(x − 4)(x + 1)

6 marks
Show answer
x2-x+8(x-4)(x+1)
8

  1. Simplify fully 2x2 + 5x − 3x2 − 9

  2. Hence, or otherwise, solve

    2x2 + 5x − 3x2 − 9 = 5

6 marks
Show answer
a) (2x - 1)/(x - 3) b) x = 14/3
9

Write 2x2 − 9 + 1x + 3 as a single fraction in its simplest form.

3 marks
Show answer
(x - 1)/(x2 - 9)
10

x + 2y3x − y = 2

Find the ratio x : y. Give your answer in the form a : b where a and b are integers.

3 marks
Show answer
4 : 5
11

Solve 3x + 2 + 4x − 1 = 1

Show all your working.

5 marks
Show answer
x) 7 x) -1

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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