Pre-Calculus 11
6.1 Rational Expressions
AN4: Determine equivalent forms of rational expressions (limited to numerators
and denominators that are monomials, binomials or trinomials).
By the end of this section you should be able to:
 Explain why a given value is non-permissible for a given rational expression.
 Determine the non-permissible values for a rational expression.
 Determine a rational expression that is equivalent to a given rational
expression by multiplying the numerator and denominator by the same
factor (limited to a monomial or a binomial), and state the non-permissible
values of the equivalent rational expression.
 Simplify a rational expression.
Rational Numbers: any number that can be written in the form
𝑚
𝑛
, 𝑛 ≠ 0.
Rational Expressions: any algebraic fraction with both the numerator and
denominator that are polynomials.
Non-permissible values: all values that make the denominator zero.
Example 1: Determine the non-permissible values for the expressions.
5𝑡
a) 4𝑠𝑟 2
3𝑥−4
b) 3𝑥(𝑥−7)
2𝑝−1
c) 𝑝2 −𝑝−12
Example 2: Simplifying Rational Expressions
Find the non-permissible values first, then simplify.
a)
36𝑎2 𝑏 3
−4𝑎𝑏 3
Pre-Calculus 11
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3𝑥−6
b) 2𝑥 2 +𝑥−10
1−𝑡
c) (𝑡−1)(𝑡+1)
2𝑦 2 +𝑦−10
d) 𝑦 2 +3𝑦−10
Example 3: Pairs of non-permissible values
Find the non-permissible expression for x, simplify the expression, evaluate for x =
2.6 and y = 1.2.
16𝑥 2 −9𝑦 2
8𝑥−6𝑦
TIPS:
 Look for opposites that can cancel and leave a -1.
 Statements such as 𝑥 ≠ 2 and 𝑥 ≠ −2 can be written as 𝑥 ≠ ±2.
Pre-Calculus 11
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