5x 2 x 6x 8 4 x 4x 10 Factor out the GCF 8x 2 y 6xy 6 12x 3 9x 2 36x 7 16x 2 y 2 8xy 2 24xy 8 40x 2 50x Section 85 ID: 782206
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Slide1
Warm-Up
Foil:
(x + 3)(x + 4) 2. (x
– 5)(x + 2)
(x – 6)(x – 8) 4. (x + 4)(x – 10)
Factor out the GCF:
8x
2
y – 6xy 6. 12x
3
– 9x
2
– 36x
7. 16x
2
y
2
+ 8xy
2
+ 24xy 8. 40x
2
+ 50x
Slide2Section 8-5
Add and Subtract Rational Expressions
Slide3Example 1
Perform the indicated operation:
a.) 12 2
5x
5x
b.) 3x 1 2x + 5 2x + 5
= 2 x
= 10 5x
= 3x + 1 2x + 5
–
+
Slide4Example 2
Find the least common multiple of
5x
2
– 45
4x2
+ 24x + 36 5(x – 3)(x + 3)
5(x2
– 9) 4(x
2 + 6x + 9)
Step 1: Factor
each polynomial.
Step 2:
Form the LCM by writing each factor to the highest power it occurs in either polynomial.
4(x + 3)(x + 3)
20(x – 3)(x + 3)
2
Slide5Example 3
Add: 3 2x
10x
2
5x
2 – 10x
2x5x(x –2)
310x2
(x – 2)(x – 2)
Step 1:
Factor the denominator.
Step 2: LCM
is 10x2(x – 2).
+
2x
2x
3x – 6
10x
2
(x – 2)
+
3
10x
2
•
+
2x
5x(x –2)
•
Step 3:
Multiply
.
+
4x
2
10x
2
(x –2)
Step 4:
Add
numerators.
4x
2
+ 3x – 6
10x
2
(x – 2)
Slide6Example 4
Simplify: 6 1
x – 5 x
3 2
x
x – 5
x(x – 5)x(x – 5)
Step 2: Multiply by the LCM.
Step 1: Find
LCM of all denominators.
+
7x – 5 x – 15
•
6x + x – 5
3(x – 5) – 2x
Step 3:
Simplify
.
=
–
x(x – 5)
Slide7Homework
Section 8-5
Pages 586 –587
1, 3, 5, 6, 10, 12,
13, 17, 18, 20, 21,
22, 27, 30, 31, 32, 35