Algebra and proofAdditional / Further Maths

Dividing algebraic terms

Divide coefficients and cancel matching letter factors.

  • Write the division as a fraction, then expand powers into repeated factors.
  • Factorise the numerical coefficients and cancel matching factors from the numerator and denominator.
  • Cancel factors, not terms in a sum. Any letter in the original denominator must be non-zero.

Example 1

Cancel common factors

Simplify the expression.

Example 2

Simplify the coefficient

Fully simplify the expression.

Remember
After cancelling all copies of a letter, the remaining factor is , not .

Your turn

Question 1

Simplify. Assume the denominator is non-zero.

Check answer
Question 2

Simplify. Assume the denominator is non-zero.

Check answer
Question 3

Simplify. Assume the denominator is non-zero.

Check answer
Question 4

Simplify. Assume the denominator is non-zero.

Check answer
Question 5

Simplify. Assume the denominator is non-zero.

Check answer
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