Algebraic Fractions (Junior Cert Mathematics): Flashcards

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Adding/Subtracting Algebraic Fractions
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Algebraic fractions

Fractions containing variables like xx or yy

Requirement to add/subtract algebraic fractions

Must have same denominator

First step with different denominators

Find a common denominator

What to add/subtract when denominators are same

The numerators only

What stays unchanged when adding/subtracting

The denominator

Final step after adding/subtracting

Simplify by factorising and cancelling

How to adjust fractions to common denominator

Multiply top and bottom by same expression

Common denominator of (x−1)(x-1) and (x+2)(x+2)

(x−1)(x+2)(x-1)(x+2)

Factorise x2−9x^2 - 9

(x−3)(x+3)(x-3)(x+3) (difference of squares)

Factorise x2−4x+4x^2 - 4x + 4

(x−2)2(x-2)^2 (perfect square trinomial)

Key caution when subtracting algebraic fractions

Be careful with negative signs

After adjusting to common denominator

Add or subtract the numerators directly

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