Edexcel IGCSE Math B 3.F Algebraic fractions Question Bank

Practise simplifying algebraic fractions by factorising, using common denominators, and reducing expressions to one fraction.

Exam points

factorise numerators and denominators before cancelling common algebraic factors
combine algebraic fractions over a common denominator and simplify the numerator
turn division by an algebraic fraction into multiplication by its reciprocal before reducing

[Maximum number: 4]

Simplify fully
$\frac{20x^4+26x^3-6x^2}{5x^2-x}.$

$\frac{20x^4+26x^3-6x^2}{5x^2-x} =\frac{2x^2(10x^2+13x-3)}{x(5x-1)}$ $10x^2+13x-3=(5x-1)(2x+3)$ $\frac{2x^2(5x-1)(2x+3)}{x(5x-1)}=2x(2x+3)$

Answer: 2x(2x+3).

Marks: M1 for common factor/long division, M1 for factorising the quadratic, A1 for cancellation/factorisation, A1ft for final polynomial.

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3.F Algebraic fractions question 1