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Learning objective overview
Master Teaching Guide coverage for this objective.
NA6-5
NZC26-P4-ALG-ER-P-Y10-01
Resources
Terminology
- quadratic trinomial
- factorise
- binomial factor
- cancel
- difference of two squares
- restriction
Task goals
- Simplify a fraction with a quadratic numerator and a linear denominator by factorising the numerator and cancelling the matching bracket, e.g. $\dfrac{x^2+7x+10}{x+2}$.
- Simplify a fraction with a linear (or constant) numerator and a quadratic denominator by factorising the denominator and cancelling the matching bracket, e.g. $\dfrac{x+6}{x^2+7x+6}$.
- Use the difference-of-two-squares factorisation $x^2-a^2=(x-a)(x+a)$ to simplify a fraction where one side is a difference of squares.
- Simplify a fraction and state the restriction on $x$ implied by the cancelled factor.
- Handle a reversed-sign linear factor, e.g. $\dfrac{x^2-16}{4-x}$, by factoring out $-1$ before cancelling.
- Verify a claimed simplification by expanding the factored form back out, or find an unknown coefficient that makes a given simplification true.
Where this fits
What leads into this objective, and where it goes next.
Before
Expanding and Factorising Algebraic Expressions
Operations with Algebraic Fractions
Expanding and Factorising Using the Distributive Law (Foundational)
You are here
Simplifying algebraic fractions with an unfactorized quadratic
Simplifying and manipulating algebraic expressions involving sums, products, differences, and positive integer powers, by: collecting like terms; factorising using common factors; factorising quadratic expressions with a leading coefficient of 1; expanding products, including multiplying a single term by a bracketed term, and multiplying two expressions each of the form ax + b, where a and b are integers; factorising by grouping (i.e. using the distributive law) (e.g. x^2 + 2x − 8 = x^2 + 4x − 2x − 8 = x(x + 4) − 2(x + 4) = (x − 2)(x + 4))
Statement▸
Also under NA6-5:
For teachers
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