Chapter 7
RATIONAL EXPRESSIONS
AND EQUATIONS
SECTION 7.1
Simplifying Rational
Expressions
A RATIONAL EXPRESSION…
… is a FRACTIONAL Expression!
 i.e., 2x + 3
x2 + 2

The DOMAIN is the set of numbers that will
not make the denominator = 0
 To find the domain: set the denominator = 0
and solve.
 Exclude the value(s) you find from the
function’s domain.

EX: FIND THE DOMAIN OF EACH


1. f(x) = 2x – 5
3x + 9
2. f(x) =
3a + 5
8a2 + 6a - 9
TO SIMPLIFY A RATIONAL EXPRESSION:
 1.
Factor the numerator and
denominator completely.
 2. Divide out (cancel) any common
factors.
 3. Multiply the remaining factors.
EX: SIMPLIFY EACH RATIONAL
EXPRESSION:


1.
3x + 6
5x + 10
3. 4x3 + 4
x2 – 1
2.
6a2 – 5ab – 6b2
3a2 – 7ab – 6b2
4. 8a3 + 6a2 + 20a + 15
8a2 + 10a + 3
TO MULTIPLY RATIONAL EXPRESSIONS
Factor everything… both numerators and
denominators.
 Divide out (cancel) common factors.
Anything in the numerator can cancel out
anything in the denominator.
 Multiply across.
 Simplify as needed.

EX: MULTIPLY



1. 10x4y2 ·
18x2y3
2.
12x3y
15x2y4
12a + 16b · 15c3d4
10c2d
15a + 20b
3. x2 + 3x – 10 · x2 – 9x + 20
x2 - 16
x2 – 25
TO DIVIDE RATIONAL EXPRESSIONS:

Multiply the first expression by the
RECIPROCAL of the 2nd expression.

5.
12y + 8 ÷ 48y + 32
10 – 4y
8y3 – 20y2

6.
y2 + y – 20 ÷ 3y2 + 19y + 20
7y2
y