Combining Algebraic Fractions

Questions that require expressing multiple algebraic fractions as a single fraction in simplest form, typically involving finding common denominators.

4 questions · Moderate -0.7

1.02k Simplify rational expressions: factorising, cancelling, algebraic division
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Edexcel C3 2006 June Q1
6 marks Moderate -0.3
  1. Simplify \(\frac { 3 x ^ { 2 } - x - 2 } { x ^ { 2 } - 1 }\).
  2. Hence, or otherwise, express \(\frac { 3 x ^ { 2 } - x - 2 } { x ^ { 2 } - 1 } - \frac { 1 } { x ( x + 1 ) }\) as a single fraction in its simplest form.
Edexcel C3 2017 June Q1
4 marks Moderate -0.8
  1. Express \(\frac { 4 x } { x ^ { 2 } - 9 } - \frac { 2 } { x + 3 }\) as a single fraction in its simplest form.
OCR C4 Q4
8 marks Moderate -0.8
4. (i) Express $$\frac { 4 x } { x ^ { 2 } - 9 } - \frac { 2 } { x + 3 }$$ as a single fraction in its simplest form.
(ii) Simplify $$\frac { x ^ { 3 } - 8 } { 3 x ^ { 2 } - 8 x + 4 }$$
OCR C4 2015 June Q1
5 marks Moderate -0.8
1
  1. Express \(\frac { 2 } { 3 - x } + \frac { 3 } { 1 + x }\) as a single fraction in its simplest form.
  2. Hence express \(\left( \frac { 2 } { 3 - x } + \frac { 3 } { 1 + x } \right) \times \frac { x ^ { 2 } + 8 x - 33 } { 121 - x ^ { 2 } }\) as a single fraction in its lowest terms.