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Adding Algebraic Fractions Flashcards
GCSE Mathematics (Edexcel) 1MA1
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Algebraic fraction
A fraction where the numerator, denominator, or both contain algebraic expressions.
Key step in adding algebraic fractions
Find a common denominator for the fractions.
Simplifying algebraic fractions
Factorise the numerator and denominator where possible, then cancel common factors.
Adding fractions with the same denominator
Add the numerators and keep the denominator the same.
Adding fractions with different denominators
Rewrite each fraction with a common denominator before adding.
Example: \( \frac{1}{x} + \frac{1}{y} \)
Common denominator is \( xy \). Rewrite as \( \frac{y}{xy} + \frac{x}{xy} = \frac{x + y}{xy} \).
Example: \( \frac{2}{x+1} + \frac{3}{x+1} \)
Denominators are the same, so add numerators: \( \frac{2+3}{x+1} = \frac{5}{x+1} \).
Example: \( \frac{1}{x} + \frac{2}{x^2} \)
Common denominator is \( x^2 \). Rewrite as \( \frac{x}{x^2} + \frac{2}{x^2} = \frac{x+2}{x^2} \).
Simplifying after adding fractions
Always check if the resulting fraction can be simplified by factorising and cancelling common factors.
Why find a common denominator?
A common denominator allows you to combine the fractions into a single fraction.
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