AE5 - Multiplication of algebraic fractions 2

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Lauren Desoysa	said	Ready to use	1 year ago
Andrew Neate	said	Needs to be tested	1 year ago

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Will Morgan 11 months, 2 weeks ago

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Andrew Neate 1 year ago

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Question statement

Expand and simplify $\displaystyle{\var{LeftMul}\times\var{RightMul}}.$

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			Name	Type	Generated Value

QuadCoeff	list	[ 3, 1 ]
Num	integer	4
Lin2Coeff	list	[ 2, 3 ]
Lin1Coeff	integer	5
Lin1	string	x+5
Lin2	string	2x+3
Quad	string	3x^2+1x
LeftMul	expression	4/(3*x^2 + 1x)
RightMulTop	expression	3x^3 + 16x^2 + 5x
RightMulBottom	expression	8x + 12
RightMul	expression	(3x^3 + 16x^2 + 5x)/(8x + 12)
Ans	expression	(x + 5)/(2x + 3)

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Generated value: `list`

[ 3, 1 ]

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Quad

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Before we multiply the fractions together first lets check if we can do any cancellation. Notice that $\var{RightMulBottom}$ has a factor of $\var{Num}$ so we can cancel this straight away.

We also have a factor of $x$ in both $\var{QuadCoeff[0]}x^2+\var{QuadCoeff[1]}x$ and $\var{RightMulTop}$ so we're now left with multiplying

$\frac1{\var{QuadCoeff[0]}x+\var{QuadCoeff[1]}}\times\frac{\simplify[all,expandBrackets]{(x+{Lin1Coeff})*({QuadCoeff[0]}x+{QuadCoeff[1]})}}{\var{Lin2Coeff[0]}x+\var{Lin2Coeff[1]}}.$

We're not necesserily done with cancellation though! To make sure that a fraction with a quadratic is simplified we have to factorise it to make sure there are no linear factors we can cancel. In this case we have

$\simplify[all,expandBrackets]{(x+{Lin1Coeff})*({QuadCoeff[0]}x+{QuadCoeff[1]})}={(x+\var{Lin1Coeff})(\var{QuadCoeff[0]}x+\var{QuadCoeff[1]})}.$

This gives us one last factor to cancel and then we can finally multiply whats left of each fraction to give us a final answer of

$\var{ans}.$

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AE5 - Multiplication of algebraic fractions 2

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Taxonomy: mathcentre

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Will Morgan 11 months, 2 weeks ago

Lauren Desoysa 1 year ago

Andrew Neate 1 year ago

Andrew Neate 1 year ago

Error in variable testing condition

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Generated value: `list`

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AE5 - Multiplication of algebraic fractions 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Will Morgan 11 months, 2 weeks ago

Lauren Desoysa 1 year ago

Andrew Neate 1 year ago

Andrew Neate 1 year ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `list`