Addition and Subtraction of Rationals

Lesson 2-6

Warm-upYou have 10 minutes to complete the half-sheet on multiplication and division of rational functions.

Refresher

Adding and Subtracting RationalsIn order to add or subtract a rational, you

must have a common denominator; that means finding the least common multiple of your denominators. If we already have a common denominator, we can add the numerators and simplify.

Example: Add the following terms3 22x 3 2x 3

3 22x 3

5

2x 3

Subtraction ExampleSubtract the followingm 9 4m 6m 3 m 3

Let’s Practice1. 5.

2.

3.

4.

2 28x 2xx 4 x 4

2 22y 4y 3 y 2y 12y 3 y 3

Least Common MultipleTo find the least common multiple, we do the

following:1. Find the prime factorization of each number.2. Find the common factors.3. Multiply each number by the factors the

other has that it does not.

Example: Find the least common multiple of 6x and 8x2.

Let’s PracticeFind the LCM of the following1. 6x and 9x2. 4x and 18x2

3. 12x3 and 84. 25x2 and 45x5

5. 6x and 12x6. 20x2 and 30x7. 10xyz and 15x2yz

Least Common DenominatorWe need to understand LCM to find the

common denominator for rational expressions in order to add or subtract them. If the denominators have nothing in common, we multiply each term by the denominator of the other term.

Example 1: Example 3: 11 + 15_

12x2 16x5

Example 2:

x 3x2 5

2 3x 2 2x

Example 1

3𝑥−3

+23 𝑥

Example 2

5𝑥𝑥−2

−3 𝑥𝑥+2

Example 3

65𝑥−10

+1

𝑥2−4

Let’s Practice1.

2.

3.

55

x 2

x 4

x 2 x 2

16

x 2

Let’s Practice4.

5.

6.