Exercise algebra.equations.rational
Description
solve a rational equation (with a variable in a divisor)
Strategy
<label name="rationalequation">
<sequence>
<rule name=""/>
<label name="rationalformtopolynomial">
<let>
<decl var="0">
<orelse>
<sequence>
<rule name="check"/>
<orelse>
<choice>
<rule name="algebra.equations.rational.division-zero"/>
<rule name="algebra.equations.rational.division-one"/>
<rule name="algebra.equations.rational.same-divisor"/>
<rule name="algebra.equations.rational.same-dividend"/>
<rule name="algebra.equations.coverup.plus"/>
<rule name="algebra.equations.coverup.minus-left"/>
<rule name="algebra.equations.coverup.minus-right"/>
<rule name="algebra.equations.coverup.negate"/>
</choice>
<choice>
<rule name="algebra.equations.rational.cross-multiply"/>
<rule name="algebra.equations.rational.multiply-one-div"/>
</choice>
</orelse>
<var var="0"/>
</sequence>
<succeed/>
</orelse>
</decl>
<var var="0"/>
</let>
</label>
<label name="higherdegree">
<sequence>
<label name="higherdegreeform">
<let>
<decl var="3">
<orelse>
<sequence>
<orelse>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.polynomial.power-factors"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.coverup.power"/>
<rule name="algebra.equations.quadratic.product-zero"/>
<rule name="algebra.equations.quadratic.same-factor"/>
<rule name="algebra.equations.coverup.times"/>
<rule name="algebra.equations.polynomial.expose-factor"/>
<rule name="algebra.equations.coverup.onevar.plus"/>
<rule name="algebra.equations.coverup.onevar.minus-left"/>
<rule name="algebra.equations.coverup.onevar.minus-right"/>
<rule name="algebra.equations.quadratic.same-con-factor"/>
<rule name="algebra.equations.polynomial.subst"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.quadratic.move-left"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
</orelse>
<var var="3"/>
</sequence>
<succeed/>
</orelse>
</decl>
<var var="3"/>
</let>
</label>
<label name="quadratic">
<label name="quadraticequationstrategy">
<let>
<decl var="4">
<orelse>
<sequence>
<orelse>
<let>
<decl var="1">
<choice>
<label name="generalform">
<choice>
<rule name="algebra.equations.quadratic.common-factor"/>
<rule name="algebra.equations.quadratic.no-lin"/>
<rule name="algebra.equations.quadratic.simpler-poly"/>
<rule name="algebra.equations.quadratic.scale" removed="true"/>
<rule name="algebra.equations.quadratic.nice-factors"/>
<rule name="algebra.equations.coverup.power"/>
</choice>
</label>
<label name="abcform">
<rule name="algebra.equations.quadratic.abc"/>
</label>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<let>
<decl var="1">
<choice>
<label name="zeroform">
<rule name="algebra.equations.quadratic.product-zero"/>
</label>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<let>
<decl var="1">
<choice>
<label name="constantform">
<choice>
<rule name="algebra.equations.coverup.onevar.plus"/>
<rule name="algebra.equations.coverup.onevar.minus-left"/>
<rule name="algebra.equations.coverup.onevar.minus-right"/>
<rule name="algebra.equations.coverup.times"/>
<rule name="algebra.equations.coverup.negate"/>
<rule name="algebra.equations.coverup.numerator"/>
<rule name="algebra.equations.quadratic.square-both"/>
<rule name="algebra.equations.quadratic.left-square"/>
</choice>
</label>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<choice>
<label name="squarerootsimplification">
<rule name="algebra.equations.quadratic.simpler-sqrt"/>
</label>
<label name="approximateresult" removed="true">
<label name="algebra.equations.quadratic.approx" collapsed="true">
<sequence>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.quadratic.approx"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<let>
<decl var="3">
<orelse>
<sequence>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.quadratic.approx"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<var var="3"/>
</sequence>
<succeed/>
</orelse>
</decl>
<var var="3"/>
</let>
</sequence>
</label>
</label>
</choice>
<label name="topform">
<orelse>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.quadratic.cancel"/>
<rule name="algebra.equations.quadratic.same-factor"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<choice>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.quadratic.same-con-factor"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<label name="algebra.equations.linear.merge" collapsed="true">
<sequence>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.linear.merge"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<let>
<decl var="3">
<orelse>
<sequence>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.linear.merge"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<var var="3"/>
</sequence>
<succeed/>
</orelse>
</decl>
<var var="3"/>
</let>
</sequence>
</label>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.quadratic.distr-square"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<label name="algebra.equations.linear.distr-times" collapsed="true">
<sequence>
<let>
<decl var="1">
<orelse>
<rule name="algebra.equations.linear.distr-times"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</orelse>
</decl>
<var var="1"/>
</let>
<let>
<decl var="3">
<orelse>
<sequence>
<let>
<decl var="1">
<orelse>
<rule name="algebra.equations.linear.distr-times"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</orelse>
</decl>
<var var="1"/>
</let>
<var var="3"/>
</sequence>
<succeed/>
</orelse>
</decl>
<var var="3"/>
</let>
</sequence>
</label>
<rule name="algebra.equations.quadratic.distr-div"/>
<let>
<decl var="1">
<choice>
<sequence>
<rule name="check"/>
<rule name="algebra.equations.linear.flip"/>
</sequence>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
</choice>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.quadratic.move-left"/>
<rule name="algebra.equations.quadratic.prepare-split" removed="true"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
</orelse>
</label>
</orelse>
<var var="4"/>
</sequence>
<succeed/>
</orelse>
</decl>
<var var="4"/>
</let>
</label>
</label>
<label name="afterwards">
<orelse>
<sequence>
<rule name="algebra.equations.polynomial.back-subst"/>
<let>
<decl var="3">
<orelse>
<sequence>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.coverup.power"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<var var="3"/>
</sequence>
<succeed/>
</orelse>
</decl>
<var var="3"/>
</let>
</sequence>
<succeed/>
</orelse>
</label>
</sequence>
</label>
<label name="checksolutions">
<orelse>
<label name="algebra.equations.rational.check-solution" collapsed="true">
<sequence>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.rational.check-solution"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<let>
<decl var="3">
<orelse>
<sequence>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.rational.check-solution"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<var var="3"/>
</sequence>
<succeed/>
</orelse>
</decl>
<var var="3"/>
</let>
</sequence>
</label>
<succeed/>
</orelse>
</label>
</sequence>
</label>Locations
| Location | Label |
| [] | rationalequation |
| [0] | ...rationalformtopolynomial |
| [0,0] | ......algebra.equations.rational.division-zero |
| [1,0] | ......algebra.equations.rational.division-one |
| [2,0] | ......algebra.equations.rational.same-divisor |
| [3,0] | ......algebra.equations.rational.same-dividend |
| [4,0] | ......algebra.equations.coverup.plus |
| [5,0] | ......algebra.equations.coverup.minus-left |
| [6,0] | ......algebra.equations.coverup.minus-right |
| [7,0] | ......algebra.equations.coverup.negate |
| [8,0] | ......algebra.equations.rational.cross-multiply |
| [9,0] | ......algebra.equations.rational.multiply-one-div |
| [1] | ...higherdegree |
| [0,1] | ......higherdegreeform |
| [0,0,1] | .........algebra.equations.polynomial.power-factors |
| [1,0,1] | .........algebra.equations.coverup.power |
| [2,0,1] | .........algebra.equations.quadratic.product-zero |
| [3,0,1] | .........algebra.equations.quadratic.same-factor |
| [4,0,1] | .........algebra.equations.coverup.times |
| [5,0,1] | .........algebra.equations.polynomial.expose-factor |
| [6,0,1] | .........algebra.equations.coverup.onevar.plus |
| [7,0,1] | .........algebra.equations.coverup.onevar.minus-left |
| [8,0,1] | .........algebra.equations.coverup.onevar.minus-right |
| [9,0,1] | .........algebra.equations.quadratic.same-con-factor |
| [10,0,1] | .........algebra.equations.polynomial.subst |
| [11,0,1] | .........algebra.equations.quadratic.move-left |
| [1,1] | ......quadratic |
| [0,1,1] | .........quadraticequationstrategy |
| [0,0,1,1] | ............generalform |
| [0,0,0,1,1] | ...............algebra.equations.quadratic.common-factor |
| [1,0,0,1,1] | ...............algebra.equations.quadratic.no-lin |
| [2,0,0,1,1] | ...............algebra.equations.quadratic.simpler-poly |
| [3,0,0,1,1] | ...............algebra.equations.quadratic.scale |
| [4,0,0,1,1] | ...............algebra.equations.quadratic.nice-factors |
| [5,0,0,1,1] | ...............algebra.equations.coverup.power |
| [1,0,1,1] | ............abcform |
| [0,1,0,1,1] | ...............algebra.equations.quadratic.abc |
| [2,0,1,1] | ............zeroform |
| [0,2,0,1,1] | ...............algebra.equations.quadratic.product-zero |
| [3,0,1,1] | ............constantform |
| [0,3,0,1,1] | ...............algebra.equations.coverup.onevar.plus |
| [1,3,0,1,1] | ...............algebra.equations.coverup.onevar.minus-left |
| [2,3,0,1,1] | ...............algebra.equations.coverup.onevar.minus-right |
| [3,3,0,1,1] | ...............algebra.equations.coverup.times |
| [4,3,0,1,1] | ...............algebra.equations.coverup.negate |
| [5,3,0,1,1] | ...............algebra.equations.coverup.numerator |
| [6,3,0,1,1] | ...............algebra.equations.quadratic.square-both |
| [7,3,0,1,1] | ...............algebra.equations.quadratic.left-square |
| [4,0,1,1] | ............squarerootsimplification |
| [0,4,0,1,1] | ...............algebra.equations.quadratic.simpler-sqrt |
| [5,0,1,1] | ............approximateresult |
| [0,5,0,1,1] | ...............algebra.equations.quadratic.approx |
| [0,0,5,0,1,1] | ..................algebra.equations.quadratic.approx |
| [1,0,5,0,1,1] | ..................algebra.equations.quadratic.approx |
| [6,0,1,1] | ............topform |
| [0,6,0,1,1] | ...............algebra.equations.quadratic.cancel |
| [1,6,0,1,1] | ...............algebra.equations.quadratic.same-factor |
| [2,6,0,1,1] | ...............algebra.equations.quadratic.same-con-factor |
| [3,6,0,1,1] | ...............algebra.equations.linear.merge |
| [0,3,6,0,1,1] | ..................algebra.equations.linear.merge |
| [1,3,6,0,1,1] | ..................algebra.equations.linear.merge |
| [4,6,0,1,1] | ...............algebra.equations.quadratic.distr-square |
| [5,6,0,1,1] | ...............algebra.equations.linear.distr-times |
| [0,5,6,0,1,1] | ..................algebra.equations.linear.distr-times |
| [1,5,6,0,1,1] | ..................algebra.equations.linear.distr-times |
| [6,6,0,1,1] | ...............algebra.equations.quadratic.distr-div |
| [7,6,0,1,1] | ...............algebra.equations.linear.flip |
| [8,6,0,1,1] | ...............algebra.equations.quadratic.move-left |
| [9,6,0,1,1] | ...............algebra.equations.quadratic.prepare-split |
| [2,1] | ......afterwards |
| [0,2,1] | .........algebra.equations.polynomial.back-subst |
| [1,2,1] | .........algebra.equations.coverup.power |
| [2] | ...checksolutions |
| [0,2] | ......algebra.equations.rational.check-solution |
| [0,0,2] | .........algebra.equations.rational.check-solution |
| [1,0,2] | .........algebra.equations.rational.check-solution |