Robinson Tuition
Grade 5 · Foundation and Higher · free GCSE maths worksheet

Solving equations with algebraic fractions

Clearing denominators first.

13 original questions, 45 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

Solve x + 32 = 5

2 marks
Show answer
x = 7
2

Solve x3 + 2 = 6

2 marks
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x = 12
3

Solve 2x − 13 = 5

2 marks
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x = 8
4

Solve x2 + x3 = 10

3 marks
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x = 12
5

Solve x + 43 = 2x − 15

3 marks
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x = 23
6

Solve 12x − 3 = 3

3 marks
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x = 7
7

Solve x + 34 + x − 13 = 8

4 marks
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x = 13
8

Solve 6x + 1 = 4x − 1

4 marks
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x = 5
9

Solve 2x + 13 − x − 42 = 2

4 marks
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x = -2
10

Solve

x + 43 + 2x − 15 = 7

3 marks
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x = 8
11

Solve

4x − 1 − 2x + 2 = 1

4 marks
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x = 4 or x = -3
12

  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
13

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)

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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