Algebraic Fraction Multiplication and Division

Simplify expressions involving multiplication or division of two rational expressions, factorising and cancelling common factors across the product or quotient.

4 questions · Moderate -0.6

1.02k Simplify rational expressions: factorising, cancelling, algebraic division
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Edexcel C3 Q1
4 marks Moderate -0.8
  1. Express
$$\frac { 3 x ^ { 2 } } { \left( 2 x ^ { 2 } + 7 x + 6 \right) } \times \frac { 7 ( 3 + 2 x ) } { 3 x ^ { 5 } }$$ as a single fraction in its simplest form.
OCR C4 2008 June Q1
6 marks Moderate -0.3
1
  1. Simplify \(\frac { \left( 2 x ^ { 2 } - 7 x - 4 \right) ( x + 1 ) } { \left( 3 x ^ { 2 } + x - 2 \right) ( x - 4 ) }\).
  2. Find the quotient and remainder when \(x ^ { 3 } + 2 x ^ { 2 } - 6 x - 5\) is divided by \(x ^ { 2 } + 4 x + 1\).
OCR C4 Q1
4 marks Moderate -0.3
  1. Express
$$\frac { 2 x } { 2 x ^ { 2 } + 3 x - 5 } \div \frac { x ^ { 3 } } { x ^ { 2 } - x }$$ as a single fraction in its simplest form.
Edexcel C3 Q37
4 marks Moderate -0.8
Express as a single fraction in its simplest form $$\frac{x^2 - 8x + 15}{x^2 - 9} \times \frac{2x^2 + 6x}{(x - 5)^2}.$$ [4]