Algebra

11.6 Adding and Subtracting

Rational Expressions

Add or Subtract then Simplify

4

14

5

4

5

9

4

9

4

5

Adding and subtracting fractions is easywhen there is a ________________________ . common denominator

Let’s see if we can add and subtract fractions with rational expressions. ..

2

7

5

51

Let’s try these together!

1)

2)

52

2

x

23

2

23

422 xx

x

xx

x

23

)2(42 xx

xx

23

242 xx

xx

23

232 xx

x

1

1

x

(2x )(x ) - - 5 1

2(x – 1)

(3x )(x ) 2 1 + -

Add or Subtract then Simplify

572

33

572

122 xx

x

xx

x

572

222 xx

x

Add or Subtract then Simplify

Try these on your own!

3)

4)

nn

n

nn

n

33

1

33

1222

nn

n

33

32 1

1

n

4

102

4

522

2

x

x

x

xx

4

)102(52

2

x

xxx

4

1032

2

x

xx

2

5

x

x

3n(n + 1)

(x )(x ) 2 5 - +

(x + 2)(x – 2)

Unlike Denominators

6

36

4

2

1

3

2

2

13

2

6

1

Rewriting vertically may help!

Find the LCD!!

. 22

. 33

The LCD is 6!

Adding or Subtracting with Unlike Denominators

28

5

6

7

xx28

5

6

7

x

x

Let’s try these together!

1)

2

2

24

1524x

28x

x

224x

1528x

2)

6

12

1x

2

x

x

)6)(1(

1212

)6)(1(x

1282

xx

x

x

xx

)6)(1(x

)1212(1282

x

xxx

)6)(1(x

2442

x

xx

.

.

Find the LCD like normal and the exponent will be the largest of the denominators!

The LCD of 6 and 8 is 24.The LCD of x and x2 is x2.Thus, the LCD of 6x and 8x2 is 24x2.

The LCD of (x – 1) and (x + 6) is (x – 1)(x + 6).

(x – 1)(x – 1)

(x + 6)(x + 6) =

Simplify if you can!

Nothing can be factored!

4x4x

33

Adding or Subtracting with Unlike Denominators

xx 6

7

3

53

x

x

6

73

53

Try these on your own!

1)

22

x2

x2

3

2

6

107

x

x

3

2

3

6

7

6

10

x

x

x

2)

x

x

x

x 1

1

2 2

)1(

)1(2 23

xx

xxxx

The LCD is 6x3.

.

.

The LCD is x(x + 1).

(x + 1)(x + 1)

= )1(

12 23

xx

xx

HW

• P. 679 #4-29

• Review tomorrow.

• Quiz 11/4-11.6 Friday