Download 9.5 adding and subtracting rational expressions

9.5
Adding and Subtracting Rational
Expressions
(Day 1)
Fractions Review: Simplify.
1.
3 1
4
 
5 5
5
2.
5 2
3
 
7 7
7
3
(3)
3.

(3)5
14
1(5)
9 5



15
3(5) 15 15
Steps for simplifying an Add/Subtract Rational Expression
1. Get the LCD
2. Get the LCD on each term
3. Simplify the TOP (Multiply out the ( ),
4. Factor and Cancel (if possible)
5
add/subtract like terms.)
10
3
7
5
1. 2  2 

2
2
2z
4z
4z
4z
2
White Boards
3
b
2.
12.

 3  b  1
b3
b3
b3
Steps for simplifying an Add/Subtract Rational Expression
1. Get the LCD
2. Get the LCD on each term
3. Simplify the TOP(Multiply out the ( ), add/subtract like terms.)
4. Factor and Cancel (if possible)
3.
6
x 2 1
( 7 )( x  1)


(x 1)( x  1)
6  7x  7
7x  13

( x  1)( x  1)
( x  1)( x  1)
White Boards
6
( 4 )( x 1)
6  4x  4  10  4 x
4. 2


( x  2)( x  1) ( x  2)( x  1)
x  3x  2
(x  2 )( x 1)
2(5  2x)

( x  2)( x  1)
Simplify.
White Boards
9
5.
2( 27 )
27(2  n )
9(2  n)
54  27n
3n( 9 )




3
2
3
3
4n 3
3n(4n )
2(6 n )
12n
12n
4
2
a
 9a  12
( a )( a  5) ( 4 )( a  3) a  5a  4a  12
6.



(a  3)(a  5)
(a  3)( a  5) (a  5)( a  3)
(a  3)( a  5)
2
2
4t
( t )( 4 ) 5t  5 
( 5 )(t  1)

7. 2
 2

2
t (t  1)
(t )(t  1)
(t )( t  1)
2
4t 2  5t  5
t 2 (t  1)
Simplify.
8.
White Boards
1
5x

2
x  5 x  4 3x  3
1
5 x (x+4)
3

3 ( x  4)( x  1) 3( x  1) (x+4)
3  5 x 2  20 x
3( x  4)( x  1)
5 x 2  20 x  3
3( x  1)( x  4)
9.5
Adding and Subtracting Rational
Expressions
(Day 2)
Simplify.
11
7 (3) 5 (2) 21 10


1.


24(3) 36(2) 72 72
72
24
6
4
3 2 2 2
36
6
6
2 3 2 3
2  2  2  3  3  72
“greatest # of times it occurs
in either one”
Or list the multiples of the smaller factor…
24,48, 72
72 is the first number that 24 and 36 go into
Find the least common multiples (LCM) of each pair of polynomials.
2. 4 x  36 and 6 x  36 x  54
2
2
Step 1: Find the prime factors of each expression.
4( x  9)
6( x  6 x  9)
4( x  3)( x  3)
6( x  3)( x  3)
2  2( x  3)( x  3)
2  3( x  3)( x  3)
2
2
Step 2: The LCM is the greatest number of times each factor
appears in either expression.
2  2( x  3)( x  3) 3( x  3)
12( x  3) ( x  3)
2
Find the least common multiples (LCM) of each pair of polynomials.
3. 2x2 – 8x + 8 and 15x2 – 60
2(x2 – 4x + 4)
15(x2 – 4)
2(x – 2)(x – 2)
15(x + 2)(x – 2)
2(x – 2)(x – 2)15(x + 2)
30(x – 2)2(x+2)
4. 3x2 – 9x – 30 and 6x + 30
3(x2 – 3x – 10)
6(x + 5)
3(x + 2)(x – 5)
6(x + 2)(x – 5)(x + 5)
White Boards
Simplify each complex fraction.
• Complex Fraction: a fraction that has a fraction
in its numerator or denominator or in both its
numerator and denominator
Step 1: First simplify the numerator and denominator.
3
 2  xy 
5.
 3



2
2 y(x) 2  xy
x


y

x
x 1(x)
x
3
3
 x 
3x
 3 • 
 
 2  xy  2  xy
Simplify each complex fraction.
White Boards
4
4
4
6.


  4 • y   4y
xy  5
5 (y) x 5
xy  5
xy  5
x

y
y (y) 1 y
2
1 2
x2
(x)
1

x2
2x
x  (x)1 x 
x
7.


•
3 (2x) 2 3
x
4x  3
4x  3
2

2 x (2x) 1 2 x
2x
2( x  2)

4x  3
Simplify each complex fraction.
yx
x
(y) 1  1 (x)
(y) xy y 2(x)
yx
x2 y2  x
xy2
8.
•


2
yx
xy
yx
(y) 1  1 (x)
2
2
(y) x y xy (x)
x2 y2
Simplify. (Review)
White Boards
2x
3
2x
3 (x-3)
4
9. 2



x  2 x  3 4 x  4 4( x  3)( x  1) 4( x  1)(x-3)
5x  9
8 x  3x  9


4( x  1)( x  3)
4( x  3)( x  1)