Partial Fractions

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Bill Foster

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Bill Foster 55 years, 4 months ago

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Name	Status	Author	Last Modified
Partial Fractions	draft	Bill Foster	06/08/2020 08:42
Partial Fractions 1	Ready to use	joshua boddy	01/06/2016 09:47
Partial Fractions 2	Ready to use	joshua boddy	01/06/2016 09:47
Partial Fractions 3 - double root	Ready to use	joshua boddy	01/06/2016 09:47
Integration with Partial Fractions 2	Ready to use	joshua boddy	01/06/2016 09:47
Integration by Partial Fractions 1 - double root	Has some problems	joshua boddy	23/02/2021 13:55
Partial Fractions: Simple Linear Factors	Ready to use	Michael Proudman	07/12/2021 10:59
Partial Fractions: Repeated Factor	Ready to use	Michael Proudman	07/12/2021 10:59
CF Maths In class test three mick paper question 7	Ready to use	Jinhua Mathias	28/08/2024 12:15
CF Maths January test mock paper Partial Fractions 3 - double root	Ready to use	Jinhua Mathias	28/08/2024 12:15
CF Maths Januaray test mock paper Partial Fractions 1	Ready to use	Jinhua Mathias	28/08/2024 12:15
Partial Fractions: Simple Linear Factors [L5]	draft	Abbi Mullins	25/07/2018 14:02
cormac's copy of CF Maths January test mock paper Partial Fractions 3 - double root	draft	cormac breen	30/10/2018 15:53
Blathnaid's copy of Partial Fractions: Simple Linear Factors	draft	Blathnaid Sheridan	13/11/2018 10:42
Blathnaid's copy of Michael's copy of Partial Fractions 3 - double root	draft	Blathnaid Sheridan	13/11/2018 10:43
Laura's copy of Partial Fractions: Repeated Factor	draft	Laura Horton	12/02/2019 16:22

There are 43 other versions that do you not have access to.

Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	6
c	integer	1
b	integer	-6
d	integer	9
nb	string	adding
a1	integer	8
a2	integer	6
s1	integer	1

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random(1..9)

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Generated value: `integer`

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1. Gap Mathematical expression
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$\simplify{({a*a2 + c*a1} * x + {a * d + c * b})/ (({a1}*x + {b}) * ({a2}*x + {d}))}$ into partial fractions.

Input the partial fractions here: Unnamed gap.

Advice

We use partial fractions to find $A$ and $B$ such that:

$\simplify[std]{({a*a2+c*a1}*x+{c*b+a*d})/(({a1}x +{b})*({a2}x+{d}))} \;\;\;=\simplify[std]{ A/({a1}x+{b})+B/({a2}x+{d})}$

Multiplying both sides of the equation by $\displaystyle \simplify[std]{1/( ({a1}x+{b})({a2}x+{d}) )}\;\;$ we obtain:

$\simplify[std]{A*({a2}x+{d})+B*({a1}x+{b}) = {a*a2+c*a1}*x+{a*d+c*b}} \Rightarrow \simplify[std]{({a2}A+{a1}B)*x+{d}*A+{b}*B={a*a2+c*a1}*x+{a*d+c*b}}$

Identifying coefficients:

Constant term: $\simplify[std]{ {d}*A+{b}*B={a*d+c*b} }$

Coefficent $x$ : $\simplify[std]{ {a2}A+{a1}B = {a*a2+c*a1} }$

On solving these equations we obtain $A = \var{a}$ and $B=\var{c}$

Which gives:

$\simplify[std]{({a*a2+c*a1}*x+{c*b+a*d})/(({a1}x +{b})*({a2}x+{d}))}\;\;= \simplify[std]{{a}/({a1}x+{b})+{c}/({a2}x+{d})}$

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This question is used in the following exams:

mathcentre: Partial fractions by Bill Foster in Bill's workspace.
Partial Fractions by Hayley Bishop in Hayley's workspace.
Maths Support: Partial fractions by Christian Lawson-Perfect in Maths Support Wiki.
Leicester: Algebraic manipulation by Bill Foster in Bill's workspace.
Bradford: Algebraic manipulation by Bill Foster in Bill's workspace.
Algebra: 1 by Aneela Arshad in Aneela's workspace.
Algebraic Fractions 1 by Aneela Arshad in Aneela's workspace.
Algebraic manipulation: 1 by Aneela Arshad in Aneela's workspace.
P10 - Algebraic & Partial Fractions by Rob Beckett in Rob's workspace.

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Taxonomy: mathcentre

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Taxonomy: Context

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Bill Foster 55 years, 4 months ago

Error in variable testing condition

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Generated value: `integer`

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Partial Fractions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Bill Foster 55 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`