Algebraic Fractions
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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
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