Mathematics Topic
Simplifying Algebraic Fractions
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Study focus - 3 things
- Algebraic fractions contain variables in the numerator, denominator, or both
- Simplifying means factorising and cancelling common factors
- Only common factors can be cancelled, not terms that are being added or subtracted
Section 1What algebraic fractions are
An algebraic fraction is a fraction with algebraic expressions, such as 6x/9 or (x^2 - 9)/(x + 3). Treat it like a number fraction, but factorise first when needed.
Section 2Cancel common factors
To simplify, cancel factors that appear in both the numerator and denominator. For example, 6x/9 = 2x/3 because both 6 and 9 divide by 3.
Section 3Factorise before cancelling
If the numerator or denominator has more than one term, factorise it first. For example, (x^2 - 9)/(x + 3) = ((x - 3)(x + 3))/(x + 3), so it simplifies to x - 3, where x is not -3.
Section 4Do not cancel terms
A common mistake is cancelling pieces from sums. In (x + 4)/(x + 2), the x terms cannot be cancelled because they are not separate factors. Addition keeps the terms joined.
Section 5Restrictions
A denominator cannot be zero. When cancelling a factor such as x + 3, remember that the original fraction was undefined when x = -3.
Examples
Simplify 12x^2 / 18x.
Cancel the common factor 6x. This gives 2x/3.
Simplify (x^2 + 5x) / x.
Factorise the numerator: x(x + 5)/x. Cancel x to get x + 5, where x is not 0.
Now let's water it
Session runs notes to flashcards to quiz back-to-back.