Download Lesson 5.1, 5.2

5.1 Rational Expression: Multiplication and Division
Rational expression is a quotient of 2 polynomials
a
,b  0
b
Ex 1) Find all numbers for which the rational expression below is not defined.
a)
2 x  41
x3
x 2  4x  9
b)
2x  5
c)
x2  9
x 2  7 x  10
Ex2) Find the domain
x2  9
x 2  7 x  10
Ex3) Find equivalent rational expression:
a ac
c
 because  1
b bc
c
1)
2)
3)
2x 2  6x  4
4)
x2 1
5)
*** Multiply rational expressions: remember to factor first and then simplify
Ex 1)
3x  2 x 5

5x  5 y x
a c ac
 
b d bd
2)
( x  y ) 3 3x  3 y
 2
x y
x  y2
3)
a 3  b 3 a 2  2ab  b 2

a 2  b 2 a 2  ab  b 2
*** Divide rational expressions: change to multiplication first, then factor and simplify if
a c a d ad
possible    
b d b c bc
Ex1) Find the reciprocal of each expression:
x3
a) The reciprocal of
is:
x5
b) The reciprocal of (x-7) is:
x 2  7 x  10 x 2  3x  10
Ex2)

2x  4
x2
Ex 3)
a 2  b 2 a 2  2ab  b 2

ab
2a 2 b 2
Ex 4)
a3  8
 (a 2  2a  4)  (a  2) 2
a2
5.2 LCMs, LCDs, Addition and Subtraction
*** To find LCM (least common multiple), factor each term then find the product of
factors with the highest exponents.
Examples:
1) Find the LCM of 18 and 30
2) Find the LCM of 12, 18, and 24
3) Find the LCM of a2b2 and 5a3b
4) Find the LCM of (y2 + 7y + 12) and (y2 + 8y + 16)
5) Find the LCM of (x2 – 9) and x3-x2-6x, and 2x2
6) Find the LCM of (a2-b2) and (2b – 2a)
*** LCD (least common denominator) is the LCM of all denominators
** Add or subtract rational expressions with the same denominator:
a c ac
 
b b
b
** Add or subtract rational expressions with the different denominators: find the LCD first
Examples: (9 problems)
1)