Simplify algebraic fractions by addition or subtraction

Combine two or more algebraic fractions using addition or subtraction into a single simplified fraction, requiring a common denominator.

25 questions · Moderate -0.6

1.02k Simplify rational expressions: factorising, cancelling, algebraic division
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Edexcel P3 2018 Specimen Q1
4 marks Moderate -0.8
  1. Express
$$\frac { 6 x + 4 } { 9 x ^ { 2 } - 4 } - \frac { 2 } { 3 x + 1 }$$ as a single fraction in its simplest form.
Edexcel C3 2006 January Q2
7 marks Moderate -0.5
  1. Express
$$\frac { 2 x ^ { 2 } + 3 x } { ( 2 x + 3 ) ( x - 2 ) } - \frac { 6 } { x ^ { 2 } - x - 2 }$$ as a single fraction in its simplest form.
Edexcel C3 2010 January Q1
4 marks Moderate -0.8
  1. Express
$$\frac { x + 1 } { 3 x ^ { 2 } - 3 } - \frac { 1 } { 3 x + 1 }$$ as a single fraction in its simplest form.
Edexcel C3 2012 June Q1
4 marks Moderate -0.8
  1. Express
$$\frac { 2 ( 3 x + 2 ) } { 9 x ^ { 2 } - 4 } - \frac { 2 } { 3 x + 1 }$$ as a single fraction in its simplest form.
Edexcel C3 2013 June Q1
4 marks Moderate -0.5
  1. Express
$$\frac { 3 x + 5 } { x ^ { 2 } + x - 12 } - \frac { 2 } { x - 3 }$$ as a single fraction in its simplest form.
Edexcel C3 2014 June Q1
4 marks Moderate -0.8
  1. Express
$$\frac { 3 } { 2 x + 3 } - \frac { 1 } { 2 x - 3 } + \frac { 6 } { 4 x ^ { 2 } - 9 }$$ as a single fraction in its simplest form.
OCR MEI C4 2010 June Q1
3 marks Easy -1.2
1 Express \(\frac { x } { x ^ { 2 } - 1 } + \frac { 2 } { x + 1 }\) as a single fraction, simplifying your answer.
OCR C4 Q2
5 marks Moderate -0.8
  1. (i) Simplify
$$\frac { x ^ { 2 } + 7 x + 12 } { 2 x ^ { 2 } + 9 x + 4 }$$ (ii) Express $$\frac { x + 4 } { 2 x ^ { 2 } + 3 x + 1 } - \frac { 2 } { 2 x + 1 }$$ as a single fraction in its simplest form.
OCR C4 Q1
4 marks Moderate -0.3
  1. Express
$$\frac { x - 10 } { ( x - 3 ) ( x + 4 ) } - \frac { x - 8 } { ( x - 3 ) ( 2 x - 1 ) }$$ as a single fraction in its simplest form.
OCR MEI C4 Q5
3 marks Easy -1.2
5 Express \(\frac { x } { x ^ { 2 } - 1 } + \frac { 2 } { x + 1 }\) as a single fraction, simplifying your answer.
OCR MEI C4 Q8
3 marks Easy -1.2
8 Express \(\frac { x } { x ^ { 2 } - 4 } + \frac { 2 } { x + 2 }\) as a single fraction, simplifying your answer.
OCR C4 2012 June Q1
6 marks Moderate -0.8
1 Simplify
  1. \(\frac { 1 - x } { x ^ { 2 } - 3 x + 2 }\),
  2. \(\frac { ( x + 1 ) } { ( x - 1 ) ( x - 3 ) } - \frac { ( x - 5 ) } { ( x - 3 ) ( x - 4 ) }\).
OCR C4 2014 June Q1
3 marks Easy -1.2
1 Express \(x + \frac { 1 } { 1 - x } + \frac { 2 } { 1 + x }\) as a single fraction, simplifying your answer.
OCR MEI Paper 3 Specimen Q1
2 marks Easy -1.8
1 Express \(\frac { 2 } { x - 1 } + \frac { 5 } { 2 x + 1 }\) as a single fraction.
OCR MEI C4 2008 June Q1
3 marks Easy -1.2
1 Express \(\frac { x } { x ^ { 2 } - 4 } + \frac { 2 } { x + 2 }\) as a single fraction, simplifying your answer.
Edexcel C3 Q12
7 marks Standard +0.3
Express \(\frac{3}{x^2 + 2x} + \frac{x - 4}{x^2 - 4}\) as a single fraction in its simplest form. [7]
Edexcel C3 Q15
5 marks Standard +0.3
Express \(\frac{y + 3}{(y + 1)(y + 2)} - \frac{y + 1}{(y + 2)(y + 3)}\) as a single fraction in its simplest form. [5]
Edexcel C3 Q20
6 marks Standard +0.3
Express \(\frac{x}{(x+1)(x+3)} + \frac{x+12}{x^2-9}\) as a single fraction in its simplest form. [6]
Edexcel C2 Q2
5 marks Moderate -0.3
Express \(\frac{y + 3}{(y + 1)(y + 2)} - \frac{y + 1}{(y + 2)(y + 3)}\) as a single fraction in its simplest form. [5]
Edexcel C2 Q4
7 marks Standard +0.3
Express \(\frac{3}{x^2 + 2x} + \frac{x - 4}{x^2 - 4}\) as a single fraction in its simplest form. [7]
Edexcel C3 Q5
7 marks Standard +0.3
Express \(\frac{3}{x^2 + 2x} + \frac{x - 4}{x^2 - 4}\) as a single fraction in its simplest form. [7]
Edexcel C3 Q2
5 marks Moderate -0.3
Express \(\frac{y+3}{(y+1)(y+2)} - \frac{y+1}{(y+2)(y+3)}\) as a single fraction in its simplest form. [5]
Edexcel C3 Q2
6 marks Standard +0.3
Express \(\frac{x}{(x+1)(x+3)} + \frac{x+12}{x^2-9}\) as a single fraction in its simplest form. [6]
Edexcel C3 Q2
9 marks Moderate -0.8
  1. Express $$\frac{4x}{x^2 - 9} - \frac{2}{x + 3}$$ as a single fraction in its simplest form. [4]
  2. Simplify $$\frac{x^3 - 8}{3x^2 - 8x + 4}.$$ [5]
OCR C4 Q1
4 marks Moderate -0.5
Express $$\frac{5x}{(x-4)(x+1)} + \frac{3}{(x-2)(x+1)}$$ as a single fraction in its simplest form. [4]