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2. (9c 4 + 6c 3 – c 2 ) ÷ 3c 2 3c 2 + 2c Warm-up
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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