Below is the code I used.

I like ...[__]{$evaluator}{20} to adjust the width

Thanks

DOCUMENT();

loadMacros("PGstandard.pl",

"MathObjects.pl",

"PGML.pl",

"AnswerFormatHelp.pl",

"PGcourse.pl",

"contextFraction.pl",

"contextLimitedRadical.pl",

"parserOneOf.pl",

"answerHints.pl"

);

TEXT(beginproblem());

$a=random(1,9,1);

$c = list_random(2,3,5,6,7,10); #square-free

$b = random(2,4,1);

$d = $b**2*$c;

$b2 = 2*$b;

$b2c = $b2*$c;

Context("LimitedRadical");

$ansA = Formula("1/($b2*sqrt($c))");

$ansB = Formula("sqrt($c)/$b2c");

$evaluator = $ansB->cmp()->withPostFilter(AnswerHints($ansA => ["Rationalize the denominator", replaceMessage=>1]));

BEGIN_PGML

Use algebra to find the exact value of the following limits. Do not use decimals.

[``\lim_{x\rightarrow [$d]} \frac{\sqrt{x}-\sqrt{[$d]}}{x-[$d]}=``][_]{$evaluator}{20}

END_PGML

BEGIN_PGML_SOLUTION

*SOLUTION*

[``\lim_{x\rightarrow [$d]} \frac{\sqrt{x}-\sqrt{[$d]}}{x-[$d]}=\frac{\sqrt{[$c]}}{[$b2c]}``]

END_PGML_SOLUTION

ENDDOCUMENT();