This document discusses rational expressions and how to add and subtract them. It defines a rational expression as the ratio of two polynomials that can be written as p/q. It provides examples of adding and subtracting fractions with the same and different denominators. It then lists the steps for adding and subtracting rational expressions, which include factoring if necessary, canceling common factors, finding the lowest common denominator (LCD), and adding or subtracting the numerators and placing the result over the common denominator. The document provides examples worked through each step to demonstrate how to add and subtract rational expressions.

2. Example:
𝑓 𝑥 =
𝑥+4
𝑥2
Rational Expressions:
 A rational expression is the ratio of
two polynomials.
 If f is a rational expression, then f can
be written in the
form p/q where p and q are
polynomials.
-Davenport University Libraries
Polynomial
Polynomial

3. Adding and subtracting fractions:
1. Same denominators:
2. Different Denominators:
The Basics:
1
5
+
2
5
=
3
5
2
3
×
4
4
−
1
4
×
3
3
=
8
12
−
3
12
=
5
12
Same
Idea!!

4. Steps for Adding and Subtracting Rational Expressions:
Factor, if necessary.
Cancel common factors, if possible.
Look at the denominator.
Simplify if possible
11
2
3
4

5. If the denominators are the same,
add or subtract the numerators and place the result over the common
denominator.
If the denominators are different,
find the LCD. Change the expressions according to the LCD and add or
subtract numerators. Place the result over the common denominator.
 LCD: Lowest Common Denominator

6. Example:
1. Factor, if necessary.
3𝑥 + 9
𝑥2 + 5𝑥 + 6
−
8
𝑥 − 2
3𝑥 + 9
𝑥2 + 5𝑥 + 6
=
3 𝑥 + 3
𝑥 + 3 𝑥 + 2
2. Cancel common factors, if possible.
3 𝑥 + 3
𝑥 + 3 𝑥 + 2
=
3
𝑥 + 2

8. 𝑥
𝑥 − 4
+
5
4 − 𝑥
𝑥−4 = −1(4−𝑥)
So our LCM = (࢞ −
૝)
𝑥
𝑥 − 4
+
5
4 − 𝑥
×
−1
−1
𝑥
𝑥−4
+
−5
𝑥−4
=
𝑥−5
𝑥−4
Another Example:

9. Sources:
1. https://davenport.libguides.com/math-skills-overview/rational-
expressions#:~:text=Definitions%3A,p%20and%20q%20are%20polynomials.
2. https://davenport.libguides.com/math-skills-overview/rational-
expressions#:~:text=Definitions%3A,p%20and%20q%20are%20polynomials.
3. https://www.slideshare.net/DawnAdams21/adding-and-subtracting-rational-
expressions-67915408

10. Thank you for listening 