Combining algebraic fractions

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

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Question statement

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

Make sure that your answer has a numerator which you input in form $(ax+b)$ with no brackets other than the ones shown.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	3
c	integer	-3
b	integer	-3
d	integer	-2
nb	string	taking away
a1	integer	6
p	integer	-7
a2	integer	8
s1	integer	-1

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Generated value: `integer`

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

Parts

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1. Gap Mathematical expression
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1. Step Information only

Gap-fill

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Express

$\simplify{{a} /((x+{p}) ({a1}x + {b})) + ({c} /( (x+{p})({a2}x + {d})))}$ as a single fraction.

Input the fraction here: Unnamed gap.

Click on Show steps if you need help. You will lose one mark of you do so.

Advice

Show steps tells us that a good choice for the denominator of the algebraic fraction we are looking for is $\simplify{(x+{p})({a1}x+{b})({a2}x+{d})}$ .

Hence we have:

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

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Taxonomy: mathcentre

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Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

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Generated value: `integer`

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Combining algebraic fractions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`