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Rational expressions and algebraic divisionAQA A-Level Maths: Flashcards

What these 14 flashcards ask

  • What is a rational expression?
  • How do you simplify a rational expression?
  • Can you cancel the x in \frac{x+3}{x+4}?
  • Simplify \frac{x^2-9}{x^2+x-12}.
  • When is a rational expression undefined?
  • How do you divide by a fraction?
  • Simplify \frac{x^2-1}{x+1}.
  • How do you add \frac{2}{x+1}+\frac{3}{x-2}?
  • Why is \frac{2}{x+1}+\frac{3}{x-2}=\frac{5}{2x-1} wrong?
  • What is an improper rational expression?
  • Divide 2x^3-5x^2+x+7 by (x-2).
  • Write \frac{2x^3-5x^2+x+7}{x-2} as quotient plus remainder.
  • What is the first step when solving an equation with fractions?
  • What must you check after solving?

Exam questions on Rational expressions and algebraic division

  1. Let R(x)=x2−9x2+x−12R(x)=\dfrac{x^2-9}{x^2+x-12}.
    Solve R(x)=2R(x)=2.2 marks
  2. Let S(x)=2x+1+3x−2S(x)=\dfrac{2}{x+1}+\dfrac{3}{x-2}.
    Find the exact values of xx for which S(x)=1S(x)=1.2 marks
  3. Let E(x)=x2+2x−15x2−4x+3÷x+5x2−1E(x)=\dfrac{x^2+2x-15}{x^2-4x+3}\div\dfrac{x+5}{x^2-1}.
    Show that E(x)E(x) simplifies to x+1x+1.3 marks
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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).