[ww-bugs] Bug 3543: New: a correct (num,den) answer is rejected

[bugzilla-daemon at webwork.maa.org]

http://bugs.webwork.maa.org/show_bug.cgi?id=3543

           Summary: a correct (num,den) answer is rejected
           Product: Problem libraries
           Version: unspecified
          Platform: Other
        OS/Version: Other
            Status: NEW
          Severity: normal
          Priority: P5
         Component: Library (OPL)
        AssignedTo: jj at asu.edu
        ReportedBy: Dick.Lane at umontana.edu
        Web browser ---
           version:


LoyolaChicago/Precalc/Chap9Tools/Connally3-9-Tools-14.pg

With seed 2741, the task is to compute
    10/(x-3) + 3/(6x-18)
and present the answer in reduced form.

As programmed,  63/(6x-18) is required while 21/(2x-6) is rejected but with 
messages "Simplify your answer further" [sic?!?]

Since Paul's custom answer checker diagnoses some errors [and has the 
misdiagnosis noted above], I defer to him for a way to fix this incorrect 
checking.

On the other hand, my choice would be to prevent this situation from arising.  
Replacing
        $d = random(2,8,2);
with
        do  {$d = random(2,8,2)}  until  (gcd($d,$b) == 1) ;
or
        do  {$d = random(2,8,1)}  until  (gcd($d,$b) == 1) ;
might be sufficient.

Another alternative would be to explicitly reduce the naive $num/$den answer 
after its pieces are computed by
    $num = Formula("$d * $a + $b")->reduce;
    $den = Formula("$d x - $cd")->reduce;
E.g.,  compute  $g = gcd($num,$d);  and do subsequent arithmetic to get reduced 
rational answer and then also show that work in the problem's Solution.

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