Combining algebraic fractions 3.1

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

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Question statement

Express the following as a single fraction.

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			Name	Type	Generated Value

a	integer	6
c	integer	9
d	integer	-3
s1	integer	1
a2	integer	1
b1	integer	-1
b2	integer	2
nb	string	adding

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Generated value: `integer`

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"Unnamed part" - prompt
"Unnamed part" → "Unnamed gap" - Correct answer

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Express

$\simplify[std]{{a}x+{b1} } +\simplify[std]{ ({c}x+{b2}) / ({a2}x + {d})}$ as a single fraction.

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Advice

The formula for adding these expressions is:

$\simplify[std]{a + (c / d) = (ad + c) / d}$

and for this exercise we have $\simplify{a={a}x+{b1}}$ , $\simplify{c={c}x+{b2}}$ , $\simplify{d={a2}x+{d}}$ .

Hence we have:

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

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Taxonomy: mathcentre

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

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Generated value: `integer`

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Combining algebraic fractions 3.1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`