View of /trunk/rochester_problib/setAlgebra05RationalExpressions/Test2_3.pg

    1 #DESCRIPTION
    2 ##  Reducing fractions by simplifying and factoring
    3 ##ENDDESCRIPTION
    4 ##
    5 ## Author:  Mark Schmitt
    6 ## Date:    2001/02 School Year
    7 ## Course:  Honors Algebra 2
    8 ##
    9 
   10 ##KEYWORDS('algebra', 'powers')
   11 
   12 DOCUMENT();        # This should be the first executable line in the problem.
   13 
   14 loadMacros(
   15 "PG.pl",
   16 "PGbasicmacros.pl",
   17 "PGchoicemacros.pl",
   18 "PGanswermacros.pl",
   19 "PGauxiliaryFunctions.pl"
   20 );
   21 
   22 TEXT(&beginproblem);
   23 $showPartialCorrectAnswers = 1;
   24 
   25 $A = non_zero_random(-9,9,1);
   26 $B = non_zero_random(-9,9,1);
   27 $C = non_zero_random(-9,9,1);
   28 $D = non_zero_random(-9,9,1);
   29 $E = non_zero_random(-9,9,1);
   30 $F = non_zero_random(-9,9,1);
   31 while ($A+$E-$C ==0 || $F-$A*$D-$C*$B ==0) {$A=non_zero_random(-9,9,1);}
   32 while (gcd($A+$E-$C,$F-$A*$D-$C*$B)>1) {$F= non_zero_random(-9,9,1);$E =non_zero_random(-9,9,1);}
   33 
   34 $lin = $B+$D;
   35 $con = $D*$B;
   36 
   37 TEXT(EV2(<<EOT));
   38 \[ \frac{$A}{x+$B} - \frac{$C}{x+$D} + \frac{$E x+$F}{x^2+$lin x +$con} = \frac{A}{B}\]
   39 where A = \{ans_rule(10)\}
   40 $BR
   41 and B = \{ans_rule(10)\}
   42 
   43 
   44 $BR
   45 EOT
   46 
   47 $ans1 = "($A+$E-$C) * x + ($F+$A*$D-$C*$B)";
   48 $ans2 = "x**2 +$lin * x + $con";
   49 
   50 &ANS(fun_cmp($ans1));
   51 &ANS(fun_cmp($ans2));
   52 
   53 ENDDOCUMENT();        # This should be the last executable line in the problem.
   54