CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 2. Polynomials and Rational Functions

=x

(^2) − 6 x+ 8 −x (^2) +x+ 12 +x (^2) − 2 x− 30
D
=x
(^2) − 8 x− 10
D
After the numerator has been entirely simplified try to factor the remaining expression and see if anything cancels
with the denominator which you now need to replace.

= 

(x+ 2 )(x− 5 )

(x+^2 )(x−^2 )(x+^3 )(x−^4 )

=(x− 2 )((xx+−^53 ))(x− 4 )

Concept Problem Revisited
Rational expressions are an extension of fractions and the operations of simplifying, adding, subtracting, multiplying
and dividing work in exactly the same way.

Vocabulary

Arational expressionis a ratio of two polynomial expressions.

Guided Practice

1. Simplify the following expression.
   x+^11 −x+^12
   x−^12 +x+^11


2. Subtract the following rational expressions.

xx−+ (^23) −x 23 (−x (^3) +x 22 )(+x 82 x−− 924 )

3. Simplify the following expression which has an infinite number of fractions nested within other fractions.

2 + −^1 −^1

2 + 2 + −−^11

2 + 2 +− 2 −^1 + (^1) ...
Answers:

1. The expression itself does not look like a rational expression, but it can be rewritten so it is more recogniz-
   able. Also working with fractions within fractions is an important skill.