Transcript 10_4 adding rational expressions TROUT 09

10.4 Addition and Subtraction: Like
Denominators
• Goal: to add and subtract rational
expressions with like denominators
To add and subtract rational
expressions with like
denominators…
• Keep the denominator and add or subtract
the numerators (just like adding like terms)
• Remember to simplify your final answer
What does it mean to be simplified?
• Your answer has to be completely factored
(the numerator and denominator) any
common factors must be canceled out
Add & Subtract Rational Expressions
7 2 72 9
 

11 11
11
11
When the denominators are the same,
add or subtract the numerators and write
the sum or difference over the common
denominator.
Add & Subtract Rational Expressions
4m 5m 4m  5m 9m



3
3
3
3
3m
Add & Subtract Rational Expressions
2
2
2
6a
4a
10a


a2 a2 a2
Add & Subtract Rational Expressions
3x2 + 4x -15
2 x  3x  7 x  x  8


2x  1
2x  1
2x  1
2
2
x  33x  5
2x  1
- 45
4
Add & Subtract Rational Expressions
3a 7a
10a
5a



4
4
4
2
Add & Subtract Rational Expressions
2
2
2
8x
2x
10x


x4 x4
x4
Add & Subtract Rational Expressions
x  4 x  10 x  18 x  3x  28


x7
x7
x7
x  7 x  4
x7
2
Factors of A•C
2
Sum=B
x+4
Subtracting RE
• When you subtract a RE remember to
distribute the minus sign to the numerator of
the 2nd RE
Subtract:
 3x
2
 
 5x  2  x  7 x  9
2
2 x  12 x  7
2

Subtract Rational Expressions
4m  5 2m  1
( 4m  5)  ( 2m  1)


m 1
m 1
m 1
2m  6
m 1
Subtract fractions:
3x ( x  4 ) 3x   x  4 


x2 x2
x2
3x  x  4
x2
2 x  4 2  x  2
2
x2
x2
Subtract fractions:
7 x  2 4 x  1 7 x  2   4 x  1


2
2
2
3x
3x
3x
7x  2  4x 1
2
3x
3 x  3 3  x  1 x  1
2
2
2
3x
x
3x
Subtract fractions:
4 x  5 2 x  1 4 x  5   2 x  1


x 1
x 1
x 1
4x  5  2x 1
x 1
2x  6
2  x  3
x 1
x 1
Subtract fractions:
2 x  4 x  3 x  2 x  12


x3
x3
2
x  3 x  3

x  6x  9

x3
x3
2
2
x3
Subtract fractions:
5 x  3x  2 3x  3x  2


2x 1
2x 1
2
2
2 x  3x  2
2x  6x  4

2x 1
2x 1
2
2



2  x  2  x  1
2x 1
Assignment
Page 443
2-32 even
Answer must be
factored