Download Aim: How do we Add and Subtract Algebraic Fractions that have

Aim: How do we Add and Subtract
Algebraic Fractions that have
different denominators?
Do Now:
3 1
4


4 6
10
Method 1
Method 2
Find a common denominator
by multiplying the
denominators
Find the lowest
common
denominator
4  6  24
LCD of 4 & 6 is 12
3 1
3 6 1 4
    
4 6 4 6 6 4
3 1
3 3 1 2
    
4 6 4 3 6 2

18 4
22 11



24 24 24 12

9
2
11


12 12 12
Aim: Rationals w/ Unlike Denominators
Course: Adv. Alg. & Trig.
Finding the LCD
LCD of
Numbers
LCD of Variable
Expressions
Each LCD includes all the factors of both
denominators
LCD of 4x & 6x2
LCD of 4 & 6
4  2 2
6  2 3
LCD  2  2  3  12
4x  2  2  x
6 x2  2  3  x  x
LCD  2  2  3  x  x  12 x 2
Find the LCD
xy; yz
xy = x · y
yz =
y·z
LCD = x · y · z
2x + 1; 4x2 - 1
(2x + 1) = (2x + 1)
4x2 – 1 = (2x +1)(2x - 1)
LCD = (2x + 1)(2x – 1)
Aim: Rationals w/ Unlike Denominators
Course: Adv. Alg. & Trig.
Finding the LCD
1
1

xy yz
1 z 1 x

  
xy z yz x
z
x
z x



xyz xyz
xyz
LCD =
xyz
6
4
4
LCD = 1(x – y)
 
6
x y 1 x y
6 x y
4
1
 


1 x y x y 1
6( x  y )
41


1( x  y ) ( x  y )1
6x  6 y  4
6( x  y )  4


1(Rationals
x  yw/)Unlike Denominatorsx  yCourse: Adv. Alg. & Trig.
Aim:
Finding the LCD
1
3
5
Find the LCD


x 2 xy y 2
2
2
1 y
3 xy 5 x
 2 2

 2 2
x
y
xy xy y x
2
2
y
3 xy
5x
 2 2
 2 2
x y
xyxy x y
2
2
y  3 xy  5 x

x2 y2
x2
xy
y2
LCD
x2 y2
=x·x
=x·
y
=
y·y
= x · x · y · y = x2y2
Aim: Rationals w/ Unlike Denominators
Course: Adv. Alg. & Trig.
Finding the LCD
10
3

3x  6 2x  4
Find the LCD
10
3
Factor the


3( x  2) 2( x  2) Denominators
10
2
3
3

 
 LCD - 6(x-2)
3( x  2) 2
2( x  2) 3
20
9


3( x  2)2 2( x  2)3
29
29


3( x  2)2 6 x  12
3x-6 = 3(x-2)
2x-4
= 2(x-2)
Aim: Rationals w/ Unlike Denominators
Course: Adv. Alg. & Trig.
LCD = 3(x-2)2 = 6(x-2) = 6x - 12
Finding the LCD
Find the LCD
x
4

2
Factor the
x  36 3 x  18
x
4 Denominators


( x  6)( x  6) 3( x  6) 3(x - 6)( x + 6)
x
3
4
x6

 

( x  6)( x  6) 3 3( x  6) x  6
x2 – 36
3x – 18
LCD
= (x – 6)(x + 6)
= 3(x – 6)
= 3(x - 6)( x + 6)
Aim: Rationals w/ Unlike Denominators
Course: Adv. Alg. & Trig.
Finding the LCD
x
3
4
x6

 

( x  6)( x  6) 3 3( x  6) x  6
3x
4( x  6)


3( x  6)( x  6) 3( x  6)( x  6)
3 x  4 x  24
3 x  4( x  6)


3( x  6)( x  6) 3( x  6)( x  6)
 x  24

3( x  6)( x  6)
x2 – 36
3x – 18
LCD
= (x – 6)(x + 6)
= 3(x – 6)
= 3(x - 6)( x + 6)
Aim: Rationals w/ Unlike Denominators
Course: Adv. Alg. & Trig.
Application Problem
Parallel
R1
flow
R1
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 1
1
1


R R1 R2
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?
Aim: Rationals w/ Unlike Denominators
Course: Adv. Alg. & Trig.