AI generatedAlgebraGCSE Higher / IGCSE Extended

Adding algebraic fractions - with different denominators

Use a common denominator that contains each denominator as a factor.

  • Use a common denominator that contains each denominator as a factor.
  • Multiply both numerator and denominator of each fraction by its missing factor.
  • Add the new numerators. Expand, collect and factorise where helpful.

Example 1

Simplify. State any excluded values.

Multiply each fraction by its missing factor, top and bottom.Combine the numerators.Expand both products.Collect the terms and the constants.

Example 2

Simplify. State any excluded values.

Multiply each fraction by its missing factor, top and bottom.Combine the numerators.Expand both products.Collect the terms and the constants.

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
Multiply each fraction by its missing factor, top and bottom.Combine the numerators.Expand both products.Collect the terms and the constants.

Restrictions from the original expression: , .

Question 2

Simplify. State any excluded values.

Check answer
Multiply each fraction by its missing factor, top and bottom.Combine the numerators.Expand both products.Collect the terms and the constants.

Restrictions from the original expression: , .

Question 3

Simplify. State any excluded values.

Check answer
Multiply each fraction by its missing factor, top and bottom.Combine the numerators.Expand both products.Collect the terms and the constants.

Restrictions from the original expression: , .

Question 4

Simplify. State any excluded values.

Check answer
Multiply each fraction by its missing factor, top and bottom.Combine the numerators.Expand both products.Collect the terms and the constants.

Restrictions from the original expression: , .

Question 5

Simplify. State any excluded values.

Check answer
Multiply each fraction by its missing factor, top and bottom.Combine the numerators.Expand both products.Collect the terms and the constants.

Restrictions from the original expression: , .

← All Algebra cardsReport a mistake