7.51 Adding Rationals with Like Denominators

Essential Question (Avid): When done with this lesson, will I be able to add and subtract rational expressions with like denominators. Will I be able to do three sample problems without help.

Reminder: What is a rational?

A rational is a math term that describes a fraction that has a variable in the denominator. For example..

4 x + 1

As described in the Essential Question, we are going to learn how to add fractions that have…

1. A variable in the denominator2. The denominators are the same

7.51 Adding Rationals with Like Denominators

Lets do a problem and see what it looks like...

3x + 1 - x + 5 2x 2x Notice: The same denominator

When the denominator is the same, CLT the numerator…

3x + 1 - x + 5 2x 2x

3x – x and 1 – 5

2x – 4 2x

Now check…Can you factor anything? (GCF)

2(x – 2) 2x

If yes, Factor. If no, you are all done.

Yes, Factor. x – 2 x

Did you get this?

7.51 Adding Rationals with Like Denominators

Please try these three by yourself. When done, show your teacher (If you are in class)

1. x + 2 + 5x – 1 4x 4x

2. x2 + 3x + 2 - x + 10 x + 4 x + 4

3. 3x – 5 + 2x – 5 x – 2 x – 2

Level 1

Level 3

Level 3

7.51 Adding Rationals with Like Denominators

Answers

1. x + 2 + 5x – 1 4x 4x

2. x2 + 3x + 2 - x + 10 x + 4 x + 4

3. 3x – 5 + 2x – 5 x – 2 x – 2

6x + 1 4x

x – 2

5

7.51 Adding Rationals with Like Denominators

How did we get our answers?

Level 1: Easy

1. x + 2 + 5x – 1 4x 4x

6x + 14x

Level 3: Hard (Why? Because you must factor your answer!)

2. x2 + 3x + 2 - x + 10 x + 4 x + 4

x2 + 2x - 8 x + 4

Now Diamond Method the numerator (How?)

(x + 4)(x – 2)

x + 4= (x – 2)

7.51 Adding Rationals with Like Denominators

If you want the last one, Mr. Wood is going to do it on the board.

Please start and turn in your Homework

7.51 Pg 443; 1-16 (Please do at least 10)