Download presentation

Presentation is loading. Please wait.

Published byMagdalen Perkins Modified over 5 years ago

1
9.5 Adding and Subtracting Rational Expressions 4/23/2014

2
Same Denominator: When adding or subtracting fractions with same denominators, add/subtract the numerators and keep the same denominator

3
Example 1 Add and Subtract with Like Denominators Perform the indicated operation. 2x2x 3 2x2x 5 + Add numerators and simplify. 2x2x 3 2x2x 5 + = 35 + 2x2x = 2x2x 8

4
Different Denominators: If the denominators are different, find the least common denominator (LCD).

5
Example 2 Find the LCD of Rational Expressions Find the least common denominator. a. 6x6x 1, 8x 38x 3 1

6
Example 2 Find the LCD of Rational Expressions Find the least common denominator. b. 1 2x 4 – 1 3x 9 +, 2x - 4 = 2(x – 2) 3x + 9 = 3(x + 3) 2: 2, 4, 6, 8… 3: 3, 6, 9, 12… LCD: 6(x-2)(x+3) (Take the LCM and multiply by the rest of their factors)

7
Example 2 Find the LCD of Rational Expressions Find the least common denominator. c. 3, x 2 – x x 2 4 –

8
Example 2 Find the LCD of Rational Expressions Find the least common denominator. x 1 + –, x 2x 1 + d.

9
Basic Example of Adding Fractions with different denominators. 4: 4, 8, 12, 16.. 3: 3, 6, 9, 12… LCD: 12 9 4 13

10
Example 3 Add with Unlike Denominators Perform the indicated operation. a. 2x2x 3 + x 2x 2 4 Find LCD :

11
Example 3 Add with Unlike Denominators Find LCD :

12
Checkpoint Add and Subtract with Unlike Denominators Perform the indicated operation. 2x2x 3 7. x 2x 2 2 + ANSWER 2x 22x 2 + 3x3x4

13
Checkpoint Add and Subtract with Unlike Denominators 8. 3 x 1 – x + + ANSWER x 2x 2 + 2x2x + 3 () x – 1 () x + 1 Perform the indicated operation.

14
Example 4 Add with Unlike Denominators

15
9.5 p.497 #10, 12, 13, 15, 16-24even, 28, 30, 33, 37, 39 Homework:

16
Checkpoint Add and Subtract with Like Denominators Perform the indicated operation. 1. 3x3x 2 3x3x 4 + ANSWER x 2 2 2. x2 – x x2 – – ANSWER – 1 x 2x2x 4 + 3. x4 + – x3 – ANSWER x4 + x3 +

17
Subtracting Polynomials

18
Example 1 Subtract with Like Denominators Subtract. x x 3 + x 2 3 + – Subtract numerators. x x 3 + x 2 3 + – = x3 + x2 –

19
Checkpoint Extra Examples 2 1. x2 – x x2 – – ANSWER – 1 x 2x2x 4 + 2. x4 + – x3 – x4 + x3 +

20
Example 2 Subtract with Unlike Denominators Subtract. 2 x 2x 2 – – 1 x 2x 2 – x – 2 4

21
Checkpoint Add and Subtract with Unlike Denominators 11 – x 2x 2 – 1x + 1 ANSWER – x – 2 () x – 1 () x + 1 Perform the indicated operation.

22
Example 2 Subtract with Unlike Denominators Subtract. 2 x 2x 2 – – 1 x 2x 2 – x – 2 4 SOLUTION The factors of are and and the factors of are and. So, the LCD is. x 2x 2 – x – 2 () x – 2 () x + 1 x 2x 2 – 4 () x – 2 () x + 2 () x + 2 () x – 2 ( ) x + 1

23
Example 2 Subtract with Unlike Denominators Rewrite using LCD. = – 2 () x + 2 () x – 2 () x + 1 () x – 2 () x + 2 () x + 2 () x + 1 = Subtract numerators. x + 2 – 2 () x + 1 () x – 2 () x + 1 () x + 2 = Distributive property x + 2 – 2x2x () x – 2 () x + 1 () x + 2 – 2 Combine like terms. = x () x – 2 () x + 1 () x + 2 – () x + 1 2 x 2x 2 – – 1 x 2x 2 – x – 24 = 12 – Factor denominators. () x – 2 () x + 1 () x – 2 () x + 2

24
9.5 p.497 # 11, 14, 29, 31, 32, 38,40, 41 Homework:

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google