11 x1 t01 04 algebraic fractions (2012)

Algebraic Fractions

Algebraic Fractions1) Always FACTORISE FIRST

2) Only cancel ( ), not parts of them

Algebraic Fractions1) Always FACTORISE FIRST

2) Only cancel ( ), not parts of them

3 2

3 316e.g. ( ) 24

a b ciab c

Algebraic Fractions1) Always FACTORISE FIRST

2) Only cancel ( ), not parts of them

3 2

3 316e.g. ( ) 24

a b ciab c

223

abc

Algebraic Fractions1) Always FACTORISE FIRST

2) Only cancel ( ), not parts of them

3 2

3 316e.g. ( ) 24

a b ciab c

223

abc

2 2

( ) 2 2ap aqiiap aq

Algebraic Fractions1) Always FACTORISE FIRST

2) Only cancel ( ), not parts of them

3 2

3 316e.g. ( ) 24

a b ciab c

223

abc

2 2

( ) 2 2ap aqiiap aq

2 2

2a p q

a p q

2

a p q p qa p q

Algebraic Fractions1) Always FACTORISE FIRST

2) Only cancel ( ), not parts of them

3 2

3 316e.g. ( ) 24

a b ciab c

223

abc

2 2

( ) 2 2ap aqiiap aq

2 2

2a p q

a p q

2

a p q p qa p q

2

p q

2

29 1 1( ) 3 1 3 2 1x xiiix x x

2

29 1 1( ) 3 1 3 2 1x xiiix x x

1

3 1 x

x

3 1 3 1x x 3 1 1x x

2

29 1 1( ) 3 1 3 2 1x xiiix x x

1

3 1 x

x

3 1 3 1x x

1 3 1 1x x

2

29 1 1( ) 3 1 3 2 1x xiiix x x

1

3 1 x

x

2 2 2

22 4 4( )

6 3ab b a ab biv

a b a

3 1 3 1x x

1 3 1 1x x

2

29 1 1( ) 3 1 3 2 1x xiiix x x

1

3 1 x

x

2 2 2

22 4 4( )

6 3ab b a ab biv

a b a

2 3=

6 a

a b 2b a b

22a b

3 1 3 1x x

1 3 1 1x x

2

29 1 1( ) 3 1 3 2 1x xiiix x x

1

3 1 x

x

2 2 2

22 4 4( )

6 3ab b a ab biv

a b a

2 3=

6 a

a b 2b a b

22a b

1=

2 2a a b

3 1 3 1x x

1 3 1 1x x

2 21 1( ) a av

a a a a

2 21 1( ) a av

a a a a

1 11 1

a aa a a a

2 21 1( ) a av

a a a a

1 11 1

a aa a a a

1. create a common denominator

“if its not there, put it down”

1 1a a a

2 21 1( ) a av

a a a a

1 11 1

a aa a a a

1. create a common denominator

“if its not there, put it down”

1 1a a a

2. compare the old denominator with the new denominator, and ask yourself;

“what’s different?”

2 21 1( ) a av

a a a a

1 11 1

a aa a a a

1. create a common denominator

“if its not there, put it down”

1 1a a a

2. compare the old denominator with the new denominator, and ask yourself;

“what’s different?”

3. that is what you multiply the numerator by

2 21 1( ) a av

a a a a

1 11 1

a aa a a a

1. create a common denominator

“if its not there, put it down”

1 1a a a

21a

2. compare the old denominator with the new denominator, and ask yourself;

“what’s different?”

3. that is what you multiply the numerator by

2 21 1( ) a av

a a a a

1 11 1

a aa a a a

1. create a common denominator

“if its not there, put it down”

1 1a a a

21a

2. compare the old denominator with the new denominator, and ask yourself;

“what’s different?”

3. that is what you multiply the numerator by

21a

2 21 1( ) a av

a a a a

1 11 1

a aa a a a

1. create a common denominator

“if its not there, put it down”

1 1a a a

21a

2. compare the old denominator with the new denominator, and ask yourself;

“what’s different?”

3. that is what you multiply the numerator by

21a

2 22 1 2 11 1

a a a aa a a

2 21 1( ) a av

a a a a

1 11 1

a aa a a a

1. create a common denominator

“if its not there, put it down”

1 1a a a

21a

2. compare the old denominator with the new denominator, and ask yourself;

“what’s different?”

3. that is what you multiply the numerator by

21a

2 22 1 2 11 1

a a a aa a a

41 1

aa a a

2 21 1( ) a av

a a a a

1 11 1

a aa a a a

1. create a common denominator

“if its not there, put it down”

1 1a a a

21a

2. compare the old denominator with the new denominator, and ask yourself;

“what’s different?”

3. that is what you multiply the numerator by

21a

2 22 1 2 11 1

a a a aa a a

41 1

aa a a

4

1 1a a

2 2 2 21 1 2( ) vi

x yx y x y

2 2 2 21 1 2( ) vi

x yx y x y

2 21 1 2

x y x yx y x y

2 2 2 21 1 2( ) vi

x yx y x y

2 21 1 2

x y x yx y x y

2 2

x y x y

2 2 2 21 1 2( ) vi

x yx y x y

2 21 1 2

x y x yx y x y

2 2

x y x y

2x y

2 2 2 21 1 2( ) vi

x yx y x y

2 21 1 2

x y x yx y x y

2 2

x y x y

2x y 2x y

2 2 2 21 1 2( ) vi

x yx y x y

2 21 1 2

x y x yx y x y

2 2

x y x y

2x y 2x y 2 x y x y

2 2 2 21 1 2( ) vi

x yx y x y

2 21 1 2

x y x yx y x y

2 2

x y x y

2x y 2x y 2 x y x y

2 2 2 2 2 2

2 22 2 2 2x xy y x xy y x y

x y x y

2 2 2 21 1 2( ) vi

x yx y x y

2 21 1 2

x y x yx y x y

2 2

x y x y

2x y 2x y 2 x y x y

2 2 2 2 2 2

2 22 2 2 2x xy y x xy y x y

x y x y

2

2 24y

x y x y

2 2 2 21 1 2( ) vi

x yx y x y

2 21 1 2

x y x yx y x y

2 2

x y x y

2x y 2x y 2 x y x y

2 2 2 2 2 2

2 22 2 2 2x xy y x xy y x y

x y x y

2

2 24y

x y x y

Exercise 1D; 1cf, 2cfil, 3cfil, 4cgk, 5cfi, 6ace, 7bdf, 8ace, 9ace etc, 11aceg, 12, 13*bc