Refresher

definition
A rational expression is an expression that is the ratio of two polynomials.

aun14

Rational expressions are algebraic fractions in which the numerator is a polynomial and the denominator is also a polynomial (usually different from the numerator). The polynomials used in creating a rational expression may contain one term (monomial), two terms (binomial), three terms (trinomial), and so on.

Examples of Rational Expressions:
Rational Expressions
(monomial/monomial)
Rational Expression
(binomial/binomial)
Rational Expression
(binomial/trinomial)
aun1
unm2
un3

reminder
Expressions that are not polynomials cannot be used in the creation of rational expressions.

For example: aun4 is not a rational expression, since aun5 is not a polynomial.


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beware Since rational expressions represent division, we must be careful to
avoid division by zero (which creates and "undefined" situation).
If a rational fraction has a variable in its denominator, we must ensure that any
value (or values) substituted for that variable will not create a zero denominator.

If it is not obvious which values will cause a division by zero error in a rational expression,
set the denominator equal to zero and solve for the variable.

Examples of "when" rational expressions may be undefined (0 on the bottom):
Rational expression: Could it possibly
be undefined? When?
Rational expression: Could it possibly
be undefined? When?
un6
Obviously, when x = 1, the denominator will be zero, making the expression undefined.

Domain:un7
un8
Set the denominator = 0
and solve.
a2 - 4 = 0
a
2 = 4

un9
For this rational expression, we must limit the x's which
may be used, to avoid a division by zero error, which
leaves the expression undefined.
For this rational expression, we must prevent two
x
-values from being used in the expression.
Domain: un10
Rational expression: Could it possibly
be undefined? When?
Rational expression: Could it possibly
be undefined? When?
un12
Set: 8 - y = 0
         8 = y


Domain: All real numbers, except y = 8.
un13
Set: x2 + x - 12 = 0
(x - 3)(x + 4) = 0
x - 3 = 0;     x = 3
x + 4 = 0;    x = -4
Domain: All real numbers, but not x = 3 and not x = -4.

When working with rational expressions,
you may see a statement indicating where the expression will be undefined.

If such information is not stated,
you may be asked to supply this information about the "domain" of the rational expression.


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