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8.5 Warm-up
12
452
2
xx
xx3.
3
1
5
32
x
x
x
x4.
5. 3
2
155
84 2
x
x
x
xx
6.
2
32
33
1032
2
2
2
xx
xx
xx
xx3
1
x
x
25
1
x
x
5
4x
33
)3)(5(2
xx
xx
8-5 Add and Subtract Rational Expressions
Adding and Subtracting with Like Denominators
xx 5
2
5
121.
x5
10
x
2
2.22
4
x
x
x
x2
3
x
x
1
2
1
222
2
xx
x3.
1
222
2
x
x 1
122
2
x
x 2
Find the LCM
1. 5x2 – 45 and 4x2 + 24x + 36
5(x2 – 9) =
5(x – 3)(x + 3)
4x2 + 24x + 36 =
4(x2 + 6x + 9) =
4(x + 3)(x + 3) = 4(x + 3)2
LCM is 20(x – 3)(x + 3)2
2. 5x3 and 10x2 – 15x
5x3 5x(2x – 3)
LCM is 5x3(2x - 3)
Step 1 – Factor each polynomial. Write the factors as products of primes.
Step 2 – Form the LCM by writing each factor to the highest power it occurs.
Find the LCM
3. 24x2 and 8x2 – 16x
(23)(3)x2 8x(x – 2) = (23)x(x-2)
LCM is 24x2(x – 2)
Add and Subtract with Unlike Denominators
4.cc
c
c 105
2
10
322
)2(5
2
10
32
cc
c
c
LCM is 10c2(c - 2)
c
c
cc
c
c
c
c 2
2
)2(5
2
)2(
)2(
10
32
)2(10
4
)2(10
632
2
2
cc
c
cc
c
)2(10
6342
2
cc
cc
5.xx 6
7
5
12
LCM is 30x
5
5
6
7
6
6
5
12xx xx 30
35
30
72
x30
107
6.LCM is 2(x – 1)(x – 3)
7.4
6
44
122
xxx
x
)2)(2(
6
)2)(2(
1
xxxx
x
LCM is (x + 2)(x + 2)(x – 2)
)2(
)2(
)2)(2(
6
)2(
)2(
)2)(2(
1
x
x
xxx
x
xx
x
)2()2(
)2(6
)2()2(
)2)(1(22
xx
x
xx
xx
)2()2(
12622
2
xx
xxx
)2()2(
1472
2
xx
xx
Simplifying Complex Fractions
8.
10
7
5
36
x
xx
3010
7
530
3036
30
x
xx
LCM is 30 216
105
x
xx
216
5
x
x
)72(3
5
x
x
9.
32
42
x
xLCM is x
xx
x
xx
x
32
42
x
x
32
42
Homework:
Page 586: 3 -36
10.
5
1
3
25
3
xx
x
)5)(3(5
1
3
2)5)(3(
5
3)5)(3(
xx
xxxx
xxx
LCM is (x – 3)(x + 5)
)3(1)5(2
)3(3
xx
x352
93
xx
x
23
93
x
x
