Chapter 14 Algebraic Fractions and Equations and Inequalities Involving Fractions
1. Day 1 Definition, Undefined fractions and Reducing to Lowest Terms
2. HW p. 330 # 3 – 15 (by 3’s),
p. 331 # 5,11,13,15,18,24,27,30,
p. 333 # 1,9,13,16,17,19
Chapter 14 Day 1
Algebraic Fractions
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Date__________Period____
Algebraic Fraction or Rational Expression is the quotient of two polynomials.
Ex.)
m
,
3
3
,
x
5 xy
,
m
2x  3
a 2  5a  4
,
x2  4
a4
3a
,
x y
Undefined Fraction – fraction where the denominator equals zero.
Check out 5 ÷0 on calculator (gives error message)
Try 6/2 = 3. How will you check it? See that 2 x 3 = 6.
But if 5/0 had an answer, then 0 x something would have to = 5.
This is impossible!!! So division by zero is impossible and the fraction is undefined.
x3
undefined?
x  5 x  14
Factor the denominator and set each factor = 0 and solve.
x 2 - 5x – 14 = 0
Ex. 1) When is the algebraic fraction
2
Reducing Fractions to Lowest Terms
A fraction is reduced to lowest terms or simplest form if the GCF of the numerator and
denominator is 1.
Factor both numerator and denominator and cancel common factors (catch the
“cousins”)
**** Be sure NOT to cancel part of adding or subtracting (Paul Bunyan).
Ex. 2)
3x
3
= (divide numerator and denominator by x)
5x
5
Ex. 3) Note:
3 x
CANNOT BE REDUCED because of the addition
5 x
Check it out!!!! Let x = 2
But
6
3
3( 2)
=
=
10
5
5( 2)
3 2
52
=
5
3
≠
10
5
2x 2  6x
=
10 x
x 2  16
Ex. 5) 2
=
x  5x  4
Ex. 6) “cousins” have exactly opposite signs such as x – 3 and 3 – x
When you cancel cousins, make one of them a (1) and the other a (-1)
Ex 4.)
x3
= -1
3 x
Note:
53
2
=
= -1
35
2
Or
Extract a -1 out of one of them and cancel
x3
=
3 x
16  a 2
Ex. 7)
=
2a  8
6b  2b 2
Ex. 8)
=
b2  9
HW p. 330 # 3 – 15 (by 3’s)
p. 331 # 5,11,13,15,18,24,27,30
p. 333 # 1,9,13,16,17,19