Algebraic Fractions worksheet
10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.
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6 marks
(a)
Write \(\frac{ 3x + 1 }{ 2 } + \frac{ 5x + 1 }{ 5 }\) as a single fraction in its simplest form.
(b)Write \(\frac{ 3x + 4 }{ 6 } - \frac{ 5x - 1 }{ 5 }\) as a single fraction in its simplest form.
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3 marks
Simplify fully \(\frac{x^2 -x - 2 }{x^2 + 2x - 8 }\)
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3 marks
Write \(\frac{x^2 - 64 }{x^2 +x - 56 }\) in its simplest form.
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6 marks
(a)
Write \(\frac{ 5 }{x - 6 } + \frac{ 7 }{x + 5 }\) as a single fraction in its simplest form.
(b)Write \(\frac{ 6 }{x + 4 } - \frac{ 7 }{x - 5 }\) as a single fraction in its simplest form.
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6 marks
(a)
Simplify \(\frac{x^2 - 9 }{x + 3 } \times \frac{ 4 }{x - 3 }\)
(b)Simplify \(\frac{x + 2 }{ 2 } \div \frac{x^2 + 8x + 12 }{ 6 }\)
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6 marks
(a)
Solve the equation \(\frac{x - 4 }{ 5 } + \frac{x - 3 }{ 6 } = 2\)
(b)Solve the equation \(\frac{ 6 }{x + 19 } = \frac{ 2 }{x + 7 }\)
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3 marks
\(\frac{x^2 +x - 6 }{x^2 + kx - 14 } = \frac{x + 3 }{x + 7 }\)
Calculate the value of \(k\).
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6 marks
(a)
Write \(\frac{ 3x - 8 }{ 3 } + \frac{ 2x + 6 }{ 7 }\) as a single fraction in its simplest form.
(b)Write \(\frac{ 4x + 3 }{ 5 } - \frac{ 3x + 5 }{ 4 }\) as a single fraction in its simplest form.
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3 marks
Simplify \(\frac{x^2 - 11x + 30 }{x^2 - 9x + 18 }\) as far as possible.
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3 marks
Write \(\frac{x^2 - 16 }{x^2 + 9x + 20 }\) in its simplest form.
Answers
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(a) \(\frac{ 25x + 7 }{ 10 }\)
(b) \(\frac{ -15x + 26 }{ 30 }\) - \(\frac{x + 1 }{x + 4 }\)
- \(\frac{x - 8 }{x - 7 }\)
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(a) \(\frac{ 12x - 17 }{(x - 6)(x + 5)}\)
(b) \(\frac{ -x - 58 }{(x + 4)(x - 5)}\) -
(a) \(4\)
(b) \(\frac{ 3 }{x + 6 }\) -
(a) \(x = 9\)
(b) \(x = -1\) - \(5\)
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(a) \(\frac{ 27x - 38 }{ 21 }\)
(b) \(\frac{ x - 13 }{ 20 }\) - \(\frac{x - 5 }{x - 3 }\)
- \(\frac{x - 4 }{x + 5 }\)