Combining algebraic fractions 5.1

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Bill Foster

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Bill Foster 55 years, 2 months ago

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Question statement

In the first part add the two algebraic fractions together and express as a single fraction over a common denominator.

In the second part add the three fractions together and express as a single fraction.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	2
cofx	integer	0
c	integer	-2
b	integer	2
d	integer	-4
ans1	integer	2
nb	string	taking away
ans3	integer	-4
a1	integer	1
a3	integer	1
a2	integer	1
c1	integer	2
con	integer	-12
ans2	integer	-16
s1	integer	-1
d1	integer	-1

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Name

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Value

xxxxxxxxxx
 
random(1..6)

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Generated value: `integer`

→ Used by:

c
cofx
con

Advice
"Part a)" - prompt
"Part a)" → "Unnamed gap" - Correct answer
"Part b)" - prompt

Parts

Part a) Gap-fill
1. Gap Mathematical expression
  Add
1. Step Information only
Part b) Gap-fill
1. Gap Mathematical expression
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Express

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

Input the fraction here: Unnamed gap.

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

Advice

The formula for {nb} fractions is :

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

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

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

Note that the first two fractions are the same as in part a). Hence we immediately have:

$\begin{eqnarray*} \simplify{{a} / ({a1}x + {b}) + ({c} / ({a2}x + {d}))+{c1}/({a3}x+{d1})}&=&\simplify[std]{({cofx} * x + {con})/ (({a1}*x + {b}) * ({a2}*x + {d}))+{c1}/({a3}x+{d1})}\\&=&\simplify[std]{((({cofx}*x+{con})({a3}x+{d1})+{c1}*({a1}*x + {b}) * ({a2}*x + {d})))/(({a1}*x + {b}) * ({a2}*x + {d})*({a3}x+{d1}))}\\&=&\simplify[std]{(({cofx*a3}x^2+{con*a3+d1*cofx}x+{con*d1})+({c1*a1*a2}x^2+{c1*(a1*d+b*a2)}x+{c1*b*d}))/(({a1}*x + {b}) * ({a2}*x + {d})*({a3}x+{d1}))}\\&=&\simplify[std]{({ans1}x^2+{ans2}x+{ans3})/(({a1}*x + {b}) * ({a2}*x + {d})*({a3}x+{d1}))}\end{eqnarray*}$

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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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Gap-fill

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Combining algebraic fractions 5.1

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`