AI generatedAlgebraGCSE Higher / IGCSE Extended

Solving equations containing algebraic fractions

Record the values that would make any original denominator zero.

  • Record the values that would make any original denominator zero.
  • Multiply the whole equation by a common denominator to remove the fractions.
  • Solve the resulting equation and reject any solution that is excluded. Check in the original equation.

Example 1

Solve the equation. State excluded values.

Multiply by both non-zero denominators.Expand both sides.Collect the terms and constants.Multiply both sides by −1.

Example 2

Solve the equation. State excluded values.

Multiply by both non-zero denominators.Expand both sides.Collect the terms and constants.Multiply both sides by −1.

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

Your turn

Question 1

Solve the equation. State excluded values.

Check answer
Multiply by both non-zero denominators.Expand both sides.Collect the terms and constants.Multiply both sides by −1.

Exclude and . The solution -1 is allowed and satisfies the original equation.

Question 2

Solve the equation. State excluded values.

Check answer
Multiply by both non-zero denominators.Expand both sides.Collect the terms and constants.Multiply both sides by −1.

Exclude and . The solution -2 is allowed and satisfies the original equation.

Question 3

Solve the equation. State excluded values.

Check answer
Multiply by both non-zero denominators.Expand both sides.Collect the terms and constants.Multiply both sides by −1.

Exclude and . The solution -3 is allowed and satisfies the original equation.

Question 4

Solve the equation. State excluded values.

Check answer
Multiply by both non-zero denominators.Expand both sides.Collect the terms and constants.Multiply both sides by −1.

Exclude and . The solution -4 is allowed and satisfies the original equation.

Question 5

Solve the equation. State excluded values.

Check answer
Multiply by both non-zero denominators.Expand both sides.Collect the terms and constants.Multiply both sides by −1.

Exclude and . The solution -5 is allowed and satisfies the original equation.

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