Download presentation

Presentation is loading. Please wait.

Published byMadeleine Chambers Modified over 4 years ago

1
**Adding and Subtracting Rational Expressions**

Goal Determine the LCM of polynomials Goal Add and Subtract Rational Expressions

2
**What is the Least Common Multiple?**

Fractions require you to find the Least Common Multiple (LCM) in order to add and subtract them! Least Common Multiple (LCM) - smallest number or polynomial into which each of the numbers or polynomials will divide evenly. The Least Common Denominator is the LCM of the denominators.

3
**Find the LCM of each set of Polynomials**

1) 12y2, 6x2 LCM = 12x2y2 2) 16ab3, 5a2b2, 20ac LCM = 80a2b3c 3) x2 – 2x, x2 - 4 LCM = x(x + 2)(x – 2) 4) x2 – x – 20, x2 + 6x + 8 LCM = (x + 4) (x – 5) (x + 2)

4
**Adding Fractions - A Review**

LCD is 12. Find equivalent fractions using the LCD. Collect the numerators, keeping the LCD.

5
**Remember: When adding or subtracting fractions, you need a common denominator!**

When Multiplying or Dividing Fractions, you don’t need a common Denominator

6
**Steps for Adding and Subtracting Rational Expressions:**

1. Factor If possible, Cancel common factors directly over each other. Get a common denominator List out factors Multiply by 1’s Add the top (combine like terms) Re-factor and simplify if possible 4. Reduce, if possible. 5. Leave the denominators in factored form.

7
**Addition and Subtraction Is the denominator the same??**

Example: Simplify Find the LCD: 6x Now, rewrite the expression using the LCD of 6x Simplify... Add the fractions... = 19 6x

8
Simplify: Example 1 6(3mn2) + 8(5n) - 7(15m)

9
**Adding and Subtracting with polynomials as denominators**

Simplify: Find the LCD: (x + 2)(x – 2) Rewrite the expression using the LCD of (x + 2)(x – 2) Simplify... – 5x – 22 (x + 2)(x – 2)

10
**Adding and Subtracting with Binomial Denominators**

(x + 1) + 3 (x + 3) 2

11
Simplify: Example 6 ** Needs a common denominator 1st! Sometimes it helps to factor the denominators to make it easier to find your LCD. LCD: 3x3(2x+1)

12
Simplify: Example 7 LCD: (x+3)2(x-3)

13
**Simplify: 3x (x - 1) - 2x (x + 2) (x + 3)(x + 2) (x + 3)(x - 1) LCD**

Example 9 3x (x - 1) - 2x (x + 2) (x + 3)(x + 2) (x + 3)(x - 1) LCD (x + 3)(x + 2)(x - 1) x ≠ -3, -2, 1

14
**Simplify: 4x (x - 2) + 5x (x - 3) (x - 3)(x - 2) (x - 2)(x - 2) LCD**

Example 10 4x (x - 2) + 5x (x - 3) (x - 3)(x - 2) (x - 2)(x - 2) LCD (x - 3)(x - 2)(x - 2) x ≠ 3, 2

15
**Simplify: (x + 3) (x - 2) - (x - 4) (x + 1) Example 11 (x - 1)(x + 1)**

LCD (x - 1)(x + 1)(x - 2) x ≠ 1, -1, 2

Similar presentations

© 2020 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