AI generatedAlgebraGCSE Higher / IGCSE Extended

Subtracting algebraic fractions - with the same denominator

Keep the common denominator and subtract the whole second numerator.

  • Keep the common denominator and subtract the whole second numerator.
  • Use brackets around a multi-term numerator so every sign changes correctly.
  • Simplify the numerator, then check for common factors and excluded values.

Example 1

Simplify. State any excluded values.

Combine the whole numerators; keep the denominator.Change both signs after the subtraction.Collect like terms in the numerator.Factorise the collected numerator, then cancel the complete common factor.

Example 2

Simplify. State any excluded values.

Combine the whole numerators; keep the denominator.Change both signs after the subtraction.Collect like terms in the numerator.

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
Combine the whole numerators; keep the denominator.Change both signs after the subtraction.Collect like terms in the numerator.

Restrictions from the original expression: .

Question 2

Simplify. State any excluded values.

Check answer
Combine the whole numerators; keep the denominator.Change both signs after the subtraction.Collect like terms in the numerator.

Restrictions from the original expression: .

Question 3

Simplify. State any excluded values.

Check answer
Combine the whole numerators; keep the denominator.Change both signs after the subtraction.Collect like terms in the numerator.

Restrictions from the original expression: .

Question 4

Simplify. State any excluded values.

Check answer
Combine the whole numerators; keep the denominator.Change both signs after the subtraction.Collect like terms in the numerator.

Restrictions from the original expression: .

Question 5

Simplify. State any excluded values.

Check answer
Combine the whole numerators; keep the denominator.Change both signs after the subtraction.Collect like terms in the numerator.

Restrictions from the original expression: .

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