20244499
Description
Mind Map by lizabeth rawson, updated more than 1 year ago
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Created by lizabeth rawson
about 5 years ago
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Algebraic fractions
- simplify
- Example
- x² - 16
__________
- x² + 2x - 8
- (x + 4) (x - 4)
__________
- (x - 2) (x + 4)
- x - 4
_______
x - 2
- you can cancel out the two (x + 4) brackets
because they are on the top and the bottom
- This is your answer
- This is your answer
- you can cancel out the two (x + 4) brackets
because they are on the top and the bottom
- x - 4
_______
x - 2
- Factorise normally with quadratics
- (x - 2) (x + 4)
- (x + 4) (x - 4)
__________
- Simplify:
- x² + 2x - 8
- x² - 16
__________
- You simplify algebraic fractions by cancelling common terms
on the top and bottom (you may have to factorise first)
- Example
- add
- Example
- what is :
- 3
____
x+3
- +
- 1
___
x-2
- 1
___
x-2
- +
- 3 (x-2)
_______
(x+3) (x-2)
- +
- 1(x+3)
_______
(x+3)(x-2)
- creating the common
denominator by
timesing both parts of
the first fraction by the
denominator of the
second, and multiplying
both sections of the
second fraction by the
denominator of the first
- creating the common
denominator by
timesing both parts of
the first fraction by the
denominator of the
second, and multiplying
both sections of the
second fraction by the
denominator of the first
- 1(x+3)
_______
(x+3)(x-2)
- 3x-6
_______
(x+3)(x-3)
- +
- x+3
_______
(x+3)(x-3)
- simplified
- simplified
- x+3
_______
(x+3)(x-3)
- 4x-3
______
(x+3)(x-2)
- This is the answer, we have dded the
two numerators together and not
changed the denominatoor
- This is the answer, we have dded the
two numerators together and not
changed the denominatoor
- +
- +
- 3
____
x+3
- what is :
- work out the common denominator. multiply the
denominator and numerator of each fraction by
whatever gives the common denominator
- add or subtract the numerators only
- add or subtract the numerators only
- Example
- divide
- Example
- x² -4
________
x²+x -12
- ÷
- 2x + 4
________
x² -3x
- 2x + 4
________
x² -3x
- x² -4
________
x²+x -12
- x
- x² -3x
_______
2x + 4
- flip the second fraction, and change the
divide to a multiply. then work the
equation as a multiply shows to the left
- flip the second fraction, and change the
divide to a multiply. then work the
equation as a multiply shows to the left
- x² -3x
_______
2x + 4
- x
- ÷
- x² -4
________
x²+x -12
- To divide, flip the second fraction and then
multiply as shown in the multiply section
- Example
- multiply
- Example
- x² -4
________
x² +x -12
- x
- x² -3x
_______
2x + 4
- x² -3x
_______
2x + 4
- (x+2)(x-2)
__________
(x+4)(x-3)
- x
- x(x-3)
_______
2(x+2)
- factorise all the terms
- factorise all the terms
- x(x-3)
_______
2(x+2)
- (x-2)
_____
(x+4)
- x
- x
___
2
- cancel all common terms
- cancel all common terms
- x
___
2
- x(x - 2)
________
2(x + 4)
- this is your answer, when
multiplying the numerators and
denominators
- this is your answer, when
multiplying the numerators and
denominators
- x
- x
- x
- x² -4
________
x² +x -12
- multiply the numerators, and the denominators seperately
- Example
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