AI generatedAlgebraGCSE Higher / IGCSE Extended

Combining fractions before factorising a numerator

Use the common denominator to combine the full numerators first.

  • Use the common denominator to combine the full numerators first.
  • Look for a factorisation of the combined numerator, such as a difference of two squares.
  • Only then cancel a common factor and retain excluded values.

Example 1

Simplify. State any excluded values.

Subtract numerators over the common denominator.Take out the common numerical factor.Factorise the difference of two squares.Cancel the common factor.

Example 2

Simplify. State any excluded values.

Subtract numerators over the common denominator.Take out the common numerical factor.Factorise the difference of two squares.Cancel the common factor.

Remember
Use the worked steps to check your method, not just the final answer.

Your turn

Question 1

Simplify. State any excluded values.

Check answer
Subtract numerators over the common denominator.Take out the common numerical factor.Factorise the difference of two squares.Cancel the common factor.

Restrictions from the original expression: .

Question 2

Simplify. State any excluded values.

Check answer
Subtract numerators over the common denominator.Take out the common numerical factor.Factorise the difference of two squares.Cancel the common factor.

Restrictions from the original expression: .

Question 3

Simplify. State any excluded values.

Check answer
Subtract numerators over the common denominator.Take out the common numerical factor.Factorise the difference of two squares.Cancel the common factor.

Restrictions from the original expression: .

Question 4

Simplify. State any excluded values.

Check answer
Subtract numerators over the common denominator.Take out the common numerical factor.Factorise the difference of two squares.Cancel the common factor.

Restrictions from the original expression: .

Question 5

Simplify. State any excluded values.

Check answer
Subtract numerators over the common denominator.Take out the common numerical factor.Factorise the difference of two squares.Cancel the common factor.

Restrictions from the original expression: .

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