Combining algebraic fractions 3.2

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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	6
c	integer	1
b	integer	-1
d	integer	6
nb	string	adding
a1	integer	1
a2	integer	1
b1	integer	-1
b2	number	3
s1	integer	1

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Express

$\simplify{({a}x+{b1}) / ({a1}x + {b}) + ({c}x+{b2}) / ({a2}x + {d})}$ 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 $\simplify{a={a}x+{b1}}$ , $\simplify{c={abs(c)}x+{abs(b2)}}$ , $\simplify{b=x+{b}}$ , $\simplify{d=x+{d}}$ .

Hence we have:

$\begin{eqnarray*}\simplify{({a}x+{b1}) / ({a1}*x + {b}) + ({c}x+{b2}) / ({a2}*x + {d})} &=& \simplify{(({a}x+{b1}) * ({a2}*x + {d}) + ({c}x+{b2}) * ({a1}*x + {b})) / (({a1}*x + {b}) * ({a2}*x + {d}))}\\ &=&\simplify[std]{ (({a*a2} * x^2 + {b1*a2+ a*d}x+{b1*d})+({a1*c}x^2+{b*c+a1*b2}x+{b*b2})) / (({a1}*x + {b}) * ({a2}*x + {d}))}\\&=&\simplify[std]{ ({a*a2 + c*a1} * x^2 + {a * d +a1*b2+b1*a2+ c * b}x+{b1*d+b*b2}) / (({a1}*x + {b}) * ({a2}*x + {d}))}\end{eqnarray*}$

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Taxonomy: mathcentre

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Bill Foster 55 years, 2 months ago

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Generated value: `integer`

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Combining algebraic fractions 3.2

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`