Algebra 10
3 marks · NormalYou are asked to subtract the two algebraic fractions below and express your answer as a single simplified fraction:
Describe the steps you will use to obtain your answer, and explain why the common denominator should be left factorised until the end.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
Explain that you find a common denominator, write both fractions with this denominator, subtract the numerators, and then fully simplify. The common denominator is (x-2)(x+1); leaving it factorised helps reveal any further simplification or 'cancellation' in the last step.
Also accept: Explanation covers process and why to leave denominator factorised
Common mistakes: Multiplying out denominator too soon; Not simplifying at the end
Show mark scheme and worked solution
Marking points
B1 · 1 mark · Describes finding a common denominator for both fractions.
M1 · 1 mark · Writes both fractions over the common denominator (x-2)(x+1) and subtracts the numerators accordingly.
A1 · 1 mark · Explains that keeping denominator factorised helps identify further simplification and reduce errors.
Worked solution
First, find the lowest common denominator, which is (x-2)(x+1).
Leaving the denominator in factorised form shows if any further cancellation is possible at the end.