1) Add rational expressions with like denominators by adding the numerators and keeping the common denominator. 2) Find the least common denominator (LCD) when denominators are different, write the expressions with the LCD, then add the numerators. 3) Simplify the sum if possible by factorizing the numerator and/or cancelling common factors in the numerator and denominator.

1. ADDITION AND
SUBTRACTION OF
RATIONAL EXPRESSION

2. PERFORM THE INDICATED OPERATION
1.
18𝑐2
15
∙
21
𝑐2
2.
𝑎2+𝑎−12
𝑎2+3𝑎−4
∙
3−𝑎
1−𝑎

3. PERFORM THE INDICATED OPERATION
1.
18𝑐2
15
∙
21
𝑐2 =
126
5
2.
𝑎2+𝑎−12
𝑎2+3𝑎−4
∙
3−𝑎
1−𝑎
=
(𝑎+4)(𝑎−3)
(𝑎−1)(𝑎+4)
𝑥
−(𝑎−3)
−(𝑎−1)
=
𝑎−3 2
𝑎−1 2 𝑜𝑟
𝑎2
− 6𝑎+9
𝑎2
− 2𝑎+1

4. COMPLETE THE TABLE BELOW
Fraction LCD Fraction with a common
denominator
Sum
1.
5
4
+
3
8
2.
1
3
+
4
5
3.
5
6
+
3
15
4.
4
18
+
5
12
5.
2
3
+
6
7

5. COMPLETE THE TABLE BELOW
Fraction LCD Fraction with a common
denominator
Sum
1.
5
4
+
3
8
8 10
8
+
3
8
13
8
2.
1
3
+
4
5
15 5
15
+
12
15
17
15
3.
5
6
+
3
15
30 25
30
+
6
30
31
30
4.
4
18
+
5
12
36 8
36
+
15
36
23
36
5.
2
3
+
6
7
21 14
21
+
18
21
32
21

6. 1. Add (or subtract) the numerators.
2. Retain common denominator.
3. Simplify the result.
HOW TO ADD OR SUBTRACT RATIONAL
EXPRESSION WITH LIKE TERMS

7. Expression Sum
1.
3𝑥
5𝑦
+
4
5𝑦
3𝑥 + 4
5𝑦
2.
9𝑚−4
8
+
3𝑚+8
8
12𝑚 + 4
8
3.
𝟗
𝑎+4
−
4
𝑎+4
5
𝑎 + 4
4.
4𝑥2
2𝑥−7
−
49
2𝑥−7
(2𝑥+7)(2𝑥−7)
2𝑥 −7
= 2x + 7
5.
4𝑏2+8𝑏−6
4𝑏2−8𝑏
−
5𝑏+4
4𝑏2−8𝑏
4𝑏2 + 3𝑏 − 2
4𝑏2 − 8𝑏

8. HOW TO ADD OR SUBTRACT RATIONAL
EXPRESSION WITH DIFFERENT DENOMINATORS
1. Find the least common denominator (LCD).
2. Write the equivalent expression of each
rational expression.
3. Add or subtract the numerators and keep the
LCD.
4. Simplify the result if possible.

9. Expression LCD Expression with a
common denominator
Sum
1.
3𝑥2
15
+
4𝑥+2
25
−
3
5
75 45𝑥2
75
+
12𝑥 + 6
75
−
45
75
45𝑥2 + 12𝑥 − 39
75
2.
1
𝑥
+
3
𝑥2 +
1
2𝑥
2x2 2𝑥
2𝑥2
+
6
2𝑥2 +
𝑥
2𝑥2
3𝑥 + 6
2𝑥2
3.
𝑎
𝑎+3
+
5
𝑎
a (a+3) 𝑎2
𝑎(𝑎+3)
+
5𝑎+15
𝑎(𝑎+3)
𝑎2
+5𝑎+15
𝑎(𝑎+3)
4.
5
𝑎2+5𝑎
−
7
3𝑎+15
3a(a+5) 5
3𝑎(𝑎 + 5)
−
7
3𝑎(𝑎 + 5)
−
2
3𝑎(𝑎 + 5)

10. PERFORM THE INDICATED OPERATION AND SIMPLIFY.
1.
5c
6
+
2c
6
2.
5
3k
+
4
3k
3.
6
h
−
5
h
4.
8p
7
−
p+14
7
5.
3q
q−4
+
12
q−4

11. PERFORM THE INDICATED OPERATION AND SIMPLIFY.
1.
5c
6
+
2c
6
=
7c
6
2.
5
3k
+
4
3k
=
9
3k
=
3
k
3.
6
h
−
5
h
=
1
h
4.
8p
7
−
p+14
7
=
7p−14
7
=
7(𝑝−2)
7
= p – 2
5.
3q
q−4
+
12
q−4
=
3𝑞+12
q−4
=
3(q+4)
q−4
= 3

12. PERFORM THE INDICATED OPERATION AND SIMPLIFY.
1.
11
3f
+
9
5f2
2.
𝑘−6
5
+
4−k
6
3.
4
d2 +
5
d
4.
7
m−6
−
1
m
5.
r
r+s
+
s
r−𝑠

13. PERFORM THE INDICATED OPERATION AND SIMPLIFY.
1.
11
3f
+
9
5f2 =
55f
15f2 +
27
15f2 =
55𝑓+27
15f2
2.
𝑘−6
5
+
4−k
6
=
6(k−6)
30
+
5(4−k)
30
=
6𝑘 −36
30
+
20−5k
30
=
k−16
30
3.
4
d2 +
5
d
=
4
d2 +
5d
d2 =
5d + 4
d2
4.
7
m−6
−
1
m
=
7m
m(m−6)
-
m−6
m(m−6)
=
6m+6
m(m−6)
5.
r
r+s
−
s
r−𝑠
=
r(r−𝑠)
(r+s)(𝑟−𝑠)
-
s(r+𝑠)
(r+s)(𝑟−𝑠)
=
𝑟2
−𝑟𝑠−𝑟𝑠−𝑠2
(r+s)(𝑟−𝑠)
=
𝑟2
−2𝑟𝑠−𝑠2
(r+s)(𝑟−𝑠)