Simplifying Rational Expressions
Simplifying rational expressions means factorising numerator and denominator, cancelling common non-zero factors, and stating restrictions where needed.
Practice This ConceptMain explanation
Teacher explanation
In algebraic fractions, cancellation is allowed only for common factors, not for separate terms. Identities help convert expressions into factor form, such as x^2-9=(x-3)(x+3). A value that makes the original denominator zero must be excluded.
Example
(x^2-9)/(x-3) = ((x-3)(x+3))/(x-3) = x+3, where x cannot be 3.
Simple analogy
Cancel factors, never pieces of sums.
Common confusion
Students cancel terms across addition or subtraction, such as cancelling x in (x+2)/x, which is not valid.
Exam tip
Factor first, cancel only full common factors, and mention the denominator restriction if the expression has variables.
Answer writing and exam use
1-mark use
Write the exact meaning of simplifying rational expressions in one clean line.
2-mark use
Define simplifying rational expressions and add one example or condition.
3-mark use
Explain simplifying rational expressions, show the method or example, and mention the common mistake.
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