CHAPTER 19 - RATIONAL EXPRESSIONS

ACCELERATED PRE-CALCULUS SUMMER STUDY GUIDE

CHAPTER 19: RATIONAL EXPRESSIONS

2 IMPORTANT DEFINITIONS

term_definition: any "math expression" that is added or subtracted.

ex. 1) 5 + 4 - 6; 5 is a term and 4 is a factor and 6 is a term.

ex. 2) 2x + 5; 2x is a term and 5 is a term.

ex. 3) -3xy - 7x + 4y + 10 ; -3xy is a term and 7x is a term and 4y is a term and 10 is a term..

factor_definition: any "math expression" that is multiplied.

ex. 1) (5)(4) ; 5 is a factor and 4 is a factor.

ex. 2) -5(x + 3) ; -5 is a factor and (x + 3) is a factor.

ex. 3) (3x - 7)(x + 3) ; (3x - 6) is a factor and (x + 3) is a factor.

SECTION 19.1: WHAT IS A RATIONAL EXPRESSION?

A "rational expression" is a fraction with variables in the numerator and/or the denominator and the variables have positive integer powers. See the examples below.

ex. 1) $\dfrac{3x+2}{7}$

ex. 2) $\dfrac{3x+5}{4x-6}$

ex. 3)

SECTION 19.2: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS

I am assuming that you know how to add, subtract, multiply, and divide numerical fractions which are basic ideas of arithmetic. All the principles you know about fractions in arithmetic apply to algebra.

ex. 1)

ex. 2)

ex. 1)

ex. 2)

SECTION 19.3: MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS

ex. 1)

ex. 2)

ex. 3)

ex. 4)

A GENERAL COMMENT ON ADDING, SUBTRACTING,
MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS

Make sure that the answer you give when adding, subtracting, multiplying and dividing is in "LOWEST TERMS." A fraction or rational expression is in lowest terms when the greatest common factor of the numerator and denominator is 1.

RULE OF CANCELLING

When simplifying a rational expression(i.e. fraction) you can only cancel common factors. YOU CANNOT CANCEL LIKE TERMS!

Comment: common factors are also called "like factors."

THE METHOD FOR REDUCING A RATIONAL
EXPRESSION TO LOWEST TERMS

FACTOR THE NUMERATOR AND DENOMIANTOR, THEN CANCEL THE COMMON FACTORS IN THE NEMERATOR AND DENOMINATOR

PLEASE NOTE THAT THE RULE OF CANCELING WAS IN CHAPTER 7.

YOU MAY WANT TO REVIEW THIS.

------------------------------------------
IMPORTANT HINTS:
------------------------------------------

At times the G.C.F. of a numerator and denominator is not clear. Here are some helpful hints:

RULE 1) When presented with all numbers in the numerator and denominator, rewriting the numerator and denominator as a product of primes is a quick way to determine what can cancel in the numerator and denominator.

RULE 2) When presented with polynomials in the numerator and the denominator make sure to check to see if one and or the other can be factored.