Warm-upDivide.1. (x6 – x5 + x4) ÷ x2

2. (9c4 + 6c3 – c2) ÷ 3c2

3. (x2 – 5x + 6) ÷ (x – 2)

4. (2x2 + 3x – 11) ÷ (x – 3)

€

x6

x2

1. (x6 – x5 + x4) ÷ x2

€

−x5

x2

€

+x4

x2

x4 – x3

Warm-up

+ x2

€

9c4

3c2

2. (9c4 + 6c3 – c2) ÷ 3c2

€

+6c3

3c2

€

−c2

3c2

€

−13

3c2 + 2c

Warm-up

3. (x2 – 5x + 6) ÷ (x – 2)Warm-up

€

x −2 x2 −5x+6)

x

x2 -2x-3x + 6

– 3

-3x + 60

x – 3

4. (2x2 + 3x – 11) ÷ (x – 3)Warm-up

€

x −3 2x2 +3x −11)

2x

2x2 -6x9x – 11

+ 9

9x - 2716

2x + 9

€

+16x −3

Section 11.4aAdding and Subtracting

Rational Expressions (NLD)Standards: 13.0Objective: I will add and subtract rational expressions with unlike denominators.

Adding Fractions:When the denominators are the same, add the numerators together.

€

25+15

€

=35

€

8x+6x

€

=14x

€

3xy2 +

4y2

€

=3x +4y2

€

a6x

+b6x

€

=a+b6x

Example 1:Add.

€

a+2b12b

+2a−3b12b

€

(a+2b)+(2a−3b)12b

€

= 12b

3a − b

Example 2:Add.

€

x +5y30x3 +

5x −4y30x3

€

(x +5y)+(5x −4y)30x3

€

= 30x3

6x + y

Example 3:Add.

€

m +3m 2 −4m +3

+6m +1

m 2 −4m +3

€

(m +3)+(6m +1)m 2 −4m +3

€

=

m 2 −4m +37m + 4

Example 4:Add.

€

2v2 −2v−3

+v+5

v2 −2v−3

€

(2)+(v+5)v2 −2v−3

€

= v2 −2v−3

v + 7

Example 5:Add.

€

3x +3x2 −9x +20

+x +5

x2 −9x +20

€

(3x +3)+(x +5)x2 −9x+20

€

=

x2 −9x +204x + 8

Subtracting Fractions:When the denominators are the same, subtract the numerators.

€

25−15

€

=15

€

8x−6x

€

=2x

€

3xy2 −

4y2

€

=3x −4y2

€

a6x

−b6x

€

=a−b6x

Example 1:Subtract.

€

4x −5y10x

−x +2y10x

€

= 10x

3x − 7y

€

=(4x −5y)+(−x −2y)

10x

Example 2:Subtract.

€

x −y30x2 −

x −6y30x2

€

=30x25y

€

=(x −y)+(−x +6y)

30x2

€

=y6x2

Example 3:Subtract.

€

r+42r2 +9r+10

−r+3

2r2 +9r+10

€

=2r2 +9r+10

1

€

=(r+4)+(−r−3)2r2 +9r+10

Example 4:Subtract.

€

3x −25x2 −25x −30

−5x −7

5x2 −25x −30

€

=5x2 −25x −30

-2x

€

=(3x −2)+(−5x +7)5x2 −25x −30

+ 5

Example 5:Subtract.

€

42b2 +3b −20

−b +6

2b2 +3b −20

€

=2b2 +3b −20

-b

€

=4 +(−b −6)2b2 +3b −20

− 2