Robinson Tuition
Grade 7 · Higher · free GCSE maths worksheet

Algebraic fractions

Simplifying, adding and multiplying.

14 original questions, 52 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

Simplify fully 2x2 + 6x4x

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

Simplify fully

x2 + 5xx2 + 8x + 15

3 marks
Show answer
xx+3
3

Simplify fully

x2 − 92x2 + 5x − 3

3 marks
Show answer
x-32x-1
4

Simplify fully 4x2 − 92x2 + x − 6

3 marks
Show answer
(2x + 3)/(x + 2)
5

Write

3x + 2 + 5x − 1

as a single fraction in its simplest form.

3 marks
Show answer
8x+7(x+2)(x-1)
6

Show that x + 1x − 1 − x − 1x + 1 can be written as 4xx2 − 1.

3 marks
Show answer
4x/(x2 - 1)
7

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)
8

Simplify fully

[x2 + 7x + 10x2 − 4] ÷ [x2 + 10x + 253x − 6]

4 marks
Show answer
3x+5
9

Show that 2x2 − 8x − 2 ÷ x + 2x simplifies to 2x.

4 marks
Show answer
2x
10

Simplify fully

[2x2 + 7x + 3x2 − 9] × [x2 − 3x4x2 − 1]

4 marks
Show answer
x2x-1
11

Solve 3x + 1 + 2x − 2 = 1
Give your answers in the form a ± √b, where a and b are integers.

5 marks
Show answer
x = 3 + √7 or x = 3 - √7
12

Simplify fully

(1 + 2x) ÷ (1 − 4x2)

4 marks
Show answer
xx-2
13

Write 1x + 2x + 1 + 3x + 2 as a single fraction.
Expand and simplify the numerator and the denominator.

5 marks
Show answer
(6x2 + 10x + 2)/(x3 + 3x2 + 2x)
14

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)

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.

All Grade 7 topics