MCR 3U1
Unit 2
Lesson 6: Adding and Subtracting Rational Expressions
Adding fractions is something you should be able to do in your sleep by now. Let’s recall how we
mathematically go about this.
To add the fractions
3 1

5 3
3 3 1 5
   
5 3 3 5
9 5
 
15 15
14

15
3 1
 we do the following:
5 3




First we find a common denominator which is 15.
We decide what number the denominator of each fraction
needs to be multiplied by in order to get 15.
We multiply the numerator and denominator by this
number for each fraction.
We now have a common denominator and we can add the
numerators together to get our answer.
We can follow this exact same process when adding rational expressions.
To add
2x x
 we do the following:
2 3
2x x

2 3
2x 3 x 2

  
2 3 3 2
6x 2x


6
6
8x

6
4x

3





Find a common denominator of 6.
Multiply the first rational expression by 3 and the second
by 2 in order to obtain a common denominator of 6.
Multiply the rational expressions.
Add the numerators
Reduce to lowest terms
Example 1: Simplify the following expressions.
a)
4
3

x2 x2
b)
4x  3 x  2

4
3
MCR 3U1
Unit 2
You will notice the often times, the denominators will not be the same. What can you do??
This is when you need to find common denominators. Both fractions must have the same
denominator before the expression can be simplified. Remember to state your restrictions!!
Example 2: Simplify the following expressions.
3
4
a)
b)
2x

5x
4x  1 2x  3

x
3x 2
c)
4
5

x  3 4 x  12
d)
2
3

x 1 x  2
e)
2
3
 2
x  3 x  5x  6
f)
3w  4
2w  3
 2
w  5w  4 w  2 w  8
2