View of /tags/rel-1-9-02/rochester_problib/setAlgebra05RationalExpressions/sw1_5_35.pg

    1 #DESCRIPTION
    2 ##  Algebra problem: Simplify expression
    3 ##ENDDESCRIPTION
    4 
    5 ##KEYWORDS('algebra', 'fraction functions')
    6 
    7 DOCUMENT();        # This should be the first executable line in the problem.
    8 
    9 loadMacros(
   10 "PG.pl",
   11 "PGbasicmacros.pl",
   12 "PGchoicemacros.pl",
   13 "PGanswermacros.pl",
   14 "PGauxiliaryFunctions.pl"
   15 );
   16 
   17 TEXT(beginproblem());
   18 
   19 $showPartialCorrectAnswers = 1;
   20 
   21 $a = random(1,2,1);
   22 $b = random(1,4,1);
   23 $c = random(4,5,1);
   24 ## 1/(x+$a)(x+$b) - 1/(x+$a)(x-$c)
   25 $b1 = $a+$b;
   26 $c1 = $a*$b;
   27 $b2 = -$a+$c;
   28 $c2 = $a*$c;
   29 
   30 BEGIN_TEXT
   31 Simplify the expression
   32 \[\frac{1}{x^2+$b1 x+$c1} - \frac{1}{x^2-$b2 x - $c2}\]
   33 and give your answer in the form of
   34 \[\frac{f(x)}{g(x)}.\]
   35 $BR
   36 Your answer for the function \(f(x)\) is : \{ans_rule(20) \}
   37 $BR
   38 Your answer for the function \(g(x)\) is : \{ans_rule(20) \}
   39 $BR
   40 END_TEXT
   41 
   42 $ans1 = "-$c-$b";
   43 $ans2 = "(x+$a)*(x+$b)*(x-$c)";
   44 
   45 ANS(fun_cmp($ans1));
   46 ANS(fun_cmp($ans2));
   47 
   48 ENDDOCUMENT();        # This should be the last executable line in the problem.