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Simplify Rational
Expressions
Rational Expression: a
fraction whose numerators
and denominators are
polynomials.
Examples:
3 , 2x , and
6 .
x + 4 x2 – 9
x2 + 1
Domain: the set of all
real numbers except
those for which the
denominator is zero.
For example: The domain of
3 is
x+4
all real numbers except -4.
Simplify Rational Expression the same
way that you reduce a fraction.
2x
5x
Divide the numerator and denominator by “x”
2
=
5
Divide the numerator and denominator by “2”
4x  8
= 2x + 4
2
Domain:x can be any real number except a
number that would make the denominator 0!
Find the domain of each expression below.
3
x4
2x
2
x 9
6
x 5
x  4
x  3
x5
How do you know when your
rational expression is reduced?
Reduced Form: when
the numerator and
denominators have no
common factors except
for ±1.
The RULE:
To simplify fractions, divide
out common factors.
REMEMBER you can’t cancel out
+(adding)
and –(subtracting)
For a,b,c any non-zero real
numbers,
ac a
ac a


bc b
bc b
Remember you can only
cancel out FACTORS!!!
Simplify the expression.
2
x
+ 4x +4
2
x -4
(x + 2)(x + 2)
(x + 2)(x – 2)
Factor each
polynomial.
What does the numerator
and denominator have in
common?
Factor out (x + 2)
The answer is: x + 2
x-2
Simplify the expression.
x2 - 7x + 12
x2 +3x - 18
(x - 4)(x – 3)
(x + 6)(x - 3)
Factor each
polynomial.
What does the numerator and
denominator have in common?
Factor out (x – 3)
The answer is: x - 4
x+6