6-1:Adding and 6-1:Adding and Subtracting Rational Subtracting Rational

ExpressionsExpressions

6-1:Adding and 6-1:Adding and Subtracting Rational Subtracting Rational

ExpressionsExpressionsUnit 6: Rational and Radical Unit 6: Rational and Radical

EquationsEquations

Recall: Multiplying and Dividing Rational Expressions.

Example 1:

You must first factor any polynomials so that they are using multiplication instead of addition and subtraction.

2 2

2 2

+ 3 -10 + 2 - 3•

- 7 + 6 + - 6

x x x x

x x x x

+ 5 - 2 + 3 -1•

+ 3 - 2 + 3 - 2

( )( ) ( )( )( )( ) ( )( )x x x x

x x x x

Once you were multiplying everything, you could then cancel out everything that matches.

Now: Adding and Subtracting Rational Expressions.

We still must factor everything that we have in the problem, but we are looking to make the denominators all the same.

Recall: Basic Fractions

2 3+

5 8To find the common denominator, you will multiply 5 and 8

2 8 3 5 16 15 16 +15 31+ = + = =

5 8 8 5 40 40 40 40

( ) ( )( ) ( )

2 3+

+ 5 + 8

x x

x x

Here, we are doing exactly the same thing, except that the denominators are expressions instead ofintegers.

This is just like what wedid on the last slide,and the common denominator is found exactly the same wayMultiply then together

2 2

2 2 2

2 + 8 3 + 5 2 +16 3 +15+ = + =

+ 5 + 8 + 8 + 5 + 5 + 8 + 8 + 5

2 +16 + 3 +15 5 + 31=

+ 8 + 5 + 8 + 5

( ) ( )( )( ) ( )( ) ( )( ) ( )( )

( )( ) ( )( )

x x x x x x x x

x x x x x x x x

x x x x x x

x x x x

If they are already using multiplication, it can make it easier, sometimes `(although I find the last slide much easier) !

2

7+1815

.x y

Exxyy

First, find the common denominator variables are easy take the largest exponent of each one every timeThen use the regular common denominator of the numbers

Multiples of each coefficient15 15, 30, 45, 60, 75, 90, 10518 18, 36, 54,72, 90

I also need x and y2

So, the common denominator is 90xy2.

Example 2:

2 2 2

7+ = +1815 90 90

.x y

Exxyy xy xy

The question you should be asking yourself now is: what do I need to turn each denominator into the common denominator?

For 15y2

For 18xy

Ex. You will do the same with subtraction.

+ 4 +12 + 4 +12- = -

2 - 8 4 -16 2 - 4 4 - 4

2 + 4 +12 2 + 8 +12= - = - =2 2 - 4 4 - 4 4 - 4 4 - 4

2 + 8 - +12 2 + 8 - -12 - 4 1= = =

4 - 4 4 - 4 4 - 4 4

( ) ( )( )( ) ( ) ( ) ( )

( )( ) ( ) ( )

x x x x

x x x x

x x x x

x x x x

x x x x x

x x x

Example 3:

Ex. Some look very hard, but if you take your time, you can solve them.

1 1-

1 1 1= - ÷ 1+ =

11+

- +1 - -÷ = =

+1 +1

( ) ( )

( )( )

x y

x y xx

y x x y x x y x x

xy x xy x xy x

Example 4:

53 +

+ 2 =10

3 -+ 7

a

a

Example 5: