1. 7.3: Addition and Subtraction of Rational Expressions
Algebra 2A
7.3: Addition and Subtraction of Rational Expressions
September 27, 2006

2. Objectives Students will be able to:
Add and subtract rational expressions
Add and subtract rational functions

3. Adding and Subtracting fractions
In order to be able to add or subtract straight across fraction, they must have
the same denominator!
So…
P + Q = P+Q
R R R
And
P - Q = P-Q

4. An example with the same denominator=
2a2 2a2 2a2
= 3-1+5
2a2
= 7

5. Another example
3y + y + 5y =
2x2 2x2 2x2

6. What if you can simplify?
After adding, if it is possible to simplify by factoring, please do!
For example:
5x + 15
x2-9 x2-9
= 5x+15
x2-9
=5(x+3)
(x+3)(x-3)
= 5
x-3

7. Practice with the same denominator and simplifying
a2-2a-8 a2-2a-8

8. What if the denominators are different?
Then you must find the least common denominator (LCD)
Write each denominator in completely factored form
Write the LCD as a product of each prime factor to the highest power that appears in either denominator
For example:
3 and 5
4x2 6xy
4x2 = 22 * x2
6xy = 2 * 3 * x * y
The LCD must have 22 * 3 * x2
LCD = 12x2y

9. How do I use the LCD? 3 + 5 LCD= 12x2y 4x2 6xy
Then rewrite the each expression so the denominator is the LCD.
(3y) (2x) 5
(3y) 4x2 (2x) 6xy
9y x
12x2y 12x2y
= 9y+10x
12x2y

10. What if the LCD is harder to find?
x2-3x-4 x2-16
(x-4)(x+1) (x+4)(x-4)
(x+4) (x+1) 8
(x+4) (x-4)(x+1) (x+1) (x+4)(x-4)
-5x x+8 = 3x-12
(x+4) (x-4)(x+1) (x+1)(x+4)(x-4) (x+4) (x-4)(x+1)
3(x-4)
(x+4) (x-4)(x+1) 3
(x+4)(x+1)

11. More about subtracting
What if a whole number is involved?
- 5
2x-1
3 - 5
(2x-1)
(2x-1) 1 2x-1 6x
2x-1 2x-1
= 6x-8

12. Adding and subtracting rational functions
h(x) = f(x) - g(x)
h(x) = f(x) + g(x)
Use the same steps as you used with adding and subtracting rational expressions.
Make sure that your signs are correct!
Remember h(1) just means plug in x=1.
Evaluate means solve….