1. Math 025 Unit 5 Section 6.3

2. The LCM of two expressions is the product of the largest powers of the factors that occur in any one factorization of the expressions
Examples:
18 = 2 · 32
The LCM of 12 and 18 is 22 · 32 = 36
12 = 22 · 3
6x3
= 2·3·x3
The LCM is
23·3·x3
12x
= 22·3· x
= 24x3
8x2
= 23·x2

3. Find the LCM of the following:
x + 3
x – 2
x2 + x – 6
= (x + 3)(x – 2)
LCM = (x + 3)(x – 2)
x2 – 5x – 14
= (x – 7)(x + 2)
x2 – 4
= (x – 2)(x + 2)
LCM = (x – 7)(x – 2)(x + 2)

4. Objective: To add and subtract fractions with the same denominators.
1. Keep the same denominator for the answer
2. Add or subtract the numerators as indicated
3. Simplify the answer if possible
7x x x x2
7x – 3x x2 – =
4x 2x2 = x =

5. Objective: To add and subtract fractions with the same denominators.
1. Keep the same denominator for the answer
2. Add or subtract the numerators as indicated
3. Simplify the answer if possible
3x2 x2 – 1
x + 4 x2 – 1 –
3x2 – x – x2 – 1 =
(3x – 4)(x + 1) =
(x + 1)(x – 1)
3x – 4 =
x – 1

6. Objective: To add and subtract fractions with the same denominators.
2x2 + 5
x2 – 3x
x – 2 – +
x2 + 2x – x2 + 2x – x2 + 2x – 3
2x2 + 5 – x2 + 3x + x – x2 + 2x – 3 =
x2 + 4x x2 + 2x – 3
(x + 3)(x + 1) (x + 3)(x – 1) = =
x x – 1 =

7. Objective: To add and subtract fractions with different denominators.
The LCD = 12x
y x
4y 3x
3y 4x
12y
16y 9y – – + + =
12x x x
12y – 16y + 9y x =
5y x =

8. Objective: To add and subtract fractions with different denominators.
The LCD = (2x – 3)(x + 1)
2x(x + 1)
1(2x – 3) 2x – – =
2x – x + 1
(2x – 3)(x + 1) (2x – 3)(x + 1)
2x(x + 1) – 1(2x – 3) (2x – 3)(x + 1) =
2x2 + 2x – 2x + 3 (2x – 3)(x + 1) =
2x2 + 3 =
(2x – 3)(x + 1)

9. Objective: To add and subtract fractions with different denominators.
The LCD = (x – 4)(x + 2) x x + = –
x2 – 2x – – x
(x – 4)(x + 2) x – 4
x + 3
3(x + 2) = –
(x – 4)(x + 2) (x – 4)(x + 2)
x + 3 – 3(x + 2) (x – 4)(x + 2)
x + 3 – 3x – 6 (x – 4)(x + 2) = =
- 2x – 3 =
(x – 4)(x + 2)

10. Objective: To add and subtract fractions with different denominators.
The LCD = x2 x2 3 x2 = + 1
x x2
x2 + 3 = x2

11. Objective: To add and subtract fractions with different denominators.2x 2x – = –
x – – x
x – (x – 3) 2x = +
x – 3 x – 3
2x + 5 =
x – 3