Aim: Rationals w/ Unlike Denominators Course: Adv. Alg. & Trig. Do Now: Aim: How do we Add and Subtract Algebraic Fractions that have different denominators? Method 2 Find the lowest common denominator Method 1 Find a common denominator by multiplying the denominators 6 1 4 3 10 4 6 1 4 3 4 4 6 1 6 6 4 3 24 6 4 24 4 24 18 12 11 24 22 6 1 4 3 2 2 6 1 3 3 4 3 12 6 & 4 is of LCD 12 2 12 9 12 11
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Aim: Rationals w/ Unlike Denominators
Course: Adv. Alg. & Trig.
Do Now:
Aim: How do we Add and Subtract Algebraic Fractions that have
different denominators?
Method 2 Find the lowest
common denominator
Method 1 Find a common denominator
by multiplying the denominators
6
1
4
3
10
4
6
1
4
3
4
4
6
1
6
6
4
3
2464
24
4
24
18
12
11
24
22
6
1
4
3
2
2
6
1
3
3
4
3
126&4 isofLCD
12
2
12
9
12
11
Aim: Rationals w/ Unlike Denominators
Course: Adv. Alg. & Trig.
Finding the LCD
Find the LCD
xy; yz 2x + 1; 4x2 - 1
LCD of Numbers
LCD of Variable Expressions
4 2 2
Each LCD includes all the factors of both denominators
4 2 2x x LCD of 4 & 6 LCD of 4x & 6x2
xy = x · yyz = y · z
LCD = x · y · z
(2x + 1) = (2x + 1) 4x2 – 1 = (2x +1)(2x - 1)
LCD = (2x + 1)(2x – 1)
2 2 3 12LCD 6 2 3
22 2 3 12LCD x x x
26 2 3x x x
Aim: Rationals w/ Unlike Denominators
Course: Adv. Alg. & Trig.
Finding the LCD
yzxy
11
x
x
yzz
z
xy
11LCD = xyz
xyz
x
xyz
z
xyz
xz
yx
46
yx
4
1
6 LCD = 1(x – y)
1
14
1
6
yxyx
yx
1)(
14
)(1
)(6
yxyx
yx
)(1
4)(6
yx
yx
yx
yx
466
Aim: Rationals w/ Unlike Denominators
Course: Adv. Alg. & Trig.
Finding the LCD
22
531
yxyx
x2 = x · xxy = x · yy2 = y · yLCD = x · x · y · y = x2y2
2
2
22
2
2
531
x
x
yxy
xy
xyy
y
x
22
2
22
2 53
yx
x
xyxy
xy
yx
y
22
22 53
yx
xxyy
Find the LCD x2y2
Aim: Rationals w/ Unlike Denominators
Course: Adv. Alg. & Trig.
Finding the LCD
42
3
63
10
xx
3x-6 = 3(x-2) 2x-4 = 2(x-2)LCD = 3(x-2)2 = 6(x-2) = 6x - 12
3
3
)2(2
3
2
2
)2(3
10
xx
)2(2
3
)2(3
10
xx
3)2(2
9
2)2(3
20
xx
126
29
2)2(3
29
xx
Factor the Denominators
Find the LCD
LCD - 6(x-2)
Aim: Rationals w/ Unlike Denominators
Course: Adv. Alg. & Trig.
Finding the LCD
183
4
362
xx
x
x2 – 36 = (x – 6)(x + 6) 3x – 18 = 3(x – 6) LCD = 3(x - 6)( x + 6)
)6(3
4
)6)(6(
xxx
x
6
6
)6(3
4
3
3
)6)(6(
x
x
xxx
x
Factor the Denominators
Find the LCD
3(x - 6)( x + 6)
Aim: Rationals w/ Unlike Denominators
Course: Adv. Alg. & Trig.
Finding the LCD
x2 – 36 = (x – 6)(x + 6) 3x – 18 = 3(x – 6) LCD = 3(x - 6)( x + 6)
)6)(6(3
)6(4
)6)(6(3
3
xx
x
xx
x
)6)(6(3
)6(43
xx
xx
)6)(6(3
2443
xx
xx
)6)(6(3
24
xx
x
6
6
)6(3
4
3
3
)6)(6(
x
x
xxx
x
Aim: Rationals w/ Unlike Denominators
Course: Adv. Alg. & Trig.
Application Problem
An electrical conductor is any piece of material that allows electricity to flow through it. Resistance is measured in units called OHMS. A resistor is an electrical conductor that is manufactured to have a certain resistance. If two resistors are connected in parallel, the the resistance of the combination R is given by the formula
where R1 and R2 are the resistances of the resistors. What is the effective resistance of a 30-ohm resistor and a 20-ohm resistor that are connected in parallel?
21
111
RRR
Parallel
flow
R1
R1
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