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Year 9AC9M9A02
Summary of important concepts

Simplifying Algebraic Fractions

Simplify algebraic expressions, expand binomial products and factorise monic quadratic expressions.

Factorise before you cancel. You can only cancel factors, never terms.

Worked example

e.g. x2−6x+8x−2\frac{x^{2}-6x+8}{x-2}
  1. Factorise top and bottom(x−2)(x−4)x−2\frac{(x-2)(x-4)}{x-2}
  2. Cancel where possible(x−2)(x−4)x−2\frac{\cancel{(x-2)}(x-4)}{\cancel{x-2}}
  3. Simplifyx−4x - 4

Practice

1
x2−4x−12x−6\frac{x^{2}-4x-12}{x-6}
Answerx+2x+2
2
x2−11x+10x−10\frac{x^{2}-11x+10}{x-10}
Answerx−1x-1
3
x2−5x−36x+4\frac{x^{2}-5x-36}{x+4}
Answerx−9x-9
4
x2−9x+3\frac{x^{2}-9}{x+3}
Answerx−3x-3
5
2x2+6xx+3\frac{2x^{2}+6x}{x+3}
Answer2x2x
6
x2+7x+12x2+3x\frac{x^{2}+7x+12}{x^{2}+3x}
Answerx+4x\frac{x+4}{x}
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