Combining algebraic fractions 6.0

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Bill Foster

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Bill Foster 55 years, 2 months ago

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Question statement

Add the following two fractions together and express as a single fraction over a common denominator.

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			Name	Type	Generated Value

a	integer	7
co1	integer	6
c	integer	-1
b	integer	1
d	number	3
nb	string	taking away
co3	number	17
a1	integer	1
p	integer	-4
co2	integer	-5
q	integer	0
r	integer	0
s1	integer	-1
a2	integer	1

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Generated value: `integer`

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Express

$\simplify[std]{{a} / ({a1}x + {b}) + (({c}x+{p}) / ({a2}x^2 +{q}x+ {d}))}$ as a single fraction.

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Advice

The formula for {nb} fractions is :

$\simplify[std]{a / b + {s1} * (c / d) = (ad + {s1} * bc) / bd}$

and for this exercise we have $\simplify{b={a1}x+{b}}$ , $\simplify{d={a2}x^2+{q}x+{d}}$ .
Hence we have:

$\begin{eqnarray*}\simplify[std]{{a} / ({a1}*x + {b}) + (({c}x+{p}) / ({a2}*x^2+{q}x + {d}))} &=& \simplify[std]{({a} * ({a2}*x^2 +{q}x+ {d}) + ({c}x+{p}) * ({a1}*x + {b})) / (({a1}*x + {b}) * ({a2}*x^2 +{q}x+ {d}))}\\& =& \simplify[std,!collectNumbers]{({a*a2} * x^2 + {a *q}x+{a*d}+{a1*c}x^2+{p*a1+b*c}x+{b*p}) / (({a1}*x + {b}) * ({a2}*x^2 +{q}x+ {d}))}\\&=&\simplify[std,!noLeadingMinus]{({co1}x^2+{co2}x+{co3})/(({a1}*x + {b}) * ({a2}*x^2 +{q}x+ {d}))}\end{eqnarray*}$

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Taxonomy: mathcentre

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Bill Foster 55 years, 2 months ago

Error in variable testing condition

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Generated value: `integer`

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Combining algebraic fractions 6.0

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Bill Foster 55 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`