General Mathematics

1. RATIONAL
FUNCTIONS,
EQUATIONS, AND
INEQUALITIES

2. POLYNOMIAL
 an expression consisting of
variables (such as x and y) and
coefficients with one or more
than one term and variables
 Examples: 𝟏, 𝒙𝟑
, 𝟑𝒙𝟐
− 𝒙 + 𝟏
and 𝒙𝟑
+ 𝟐𝒙𝒚𝒛𝟐
− 𝒚𝒛 + 𝟏
an expression
that can be
written as a
ratio of two
polynomials

3. The variable of any
term has a negative
exponent.
CONDITIONS
WHERE AN
EXPRESSION
IS NOT
CONSIDERE
D AS A
POLYNOMIA
L:
4𝑥−3
+ 2𝑥2
− 5

4. The variable of any
term is inside the
radical symbol.
CONDITIONS
WHERE AN
EXPRESSION
IS NOT
CONSIDERE
D AS A
POLYNOMIA
L:
4𝑥2
− 𝑥

5. The variable of any
term has a fraction as
exponent.
CONDITIONS
WHERE AN
EXPRESSION
IS NOT
CONSIDERE
D AS A
POLYNOMIA
L:
𝑥
2
3 + 3𝑥 − 1

6. Therefore, if an
expression
(whether the
numerator or
denominator) is
not a
polynomial,
then it is not a
RATIONAL
EXPRESSION.
4𝑥−3
+ 2𝑥2
− 5
4𝑥2
− 𝑥
𝑥
2
3 + 3𝑥 − 1

7. an equation
involving
rational
expression
only uses =
symbol
(equal sign)
a rational
expression
combines with
any of these
inequality
symbols <, >,
≤, or ≥
a function of the
form 𝒇 𝒙 =
𝒑(𝒙)
𝒒(𝒙)
,
where 𝒑(𝒙) and 𝒒 𝒙
are polynomial
functions , and 𝒒(𝒙)
is not a zero function
The domain of 𝒇(𝒙)
is all values of 𝒙
where 𝒒(𝒙) ≠ 𝟎
RATIONAL
EQUATION
RATIONAL
INEQUALITY
RATIONAL
FUNCTION

8. 𝟑
𝒙
−
𝟐
𝟑𝒙
=
𝟏
𝒙
𝒙𝟑
+ 𝟑𝒙 − 𝟐
𝒙
=
𝟑
𝒙
𝒙 − 𝟐
𝟒𝒙
< 𝟓
𝟒
𝒙𝟐 − 𝟑𝒙 + 𝟒
≥
𝟑
𝒙
𝒇 𝒙 =
𝒙𝟐 − 𝟐𝒙 − 𝟑
𝒙 + 𝟐
or
𝒚 =
𝒙𝟐
− 𝟐𝒙 − 𝟑
𝒙 + 𝟐
RATIONAL
EQUATION
RATIONAL
INEQUALITY
RATIONAL
FUNCTION

9. SOLVING RATIONAL EQUATIONS
1.
3
4
=
x
4
2.
2
x
−
3
2x
=
1
5
3.
x
x+2
−
1
𝑥−2
=
8
𝑥2−4