I have run into an issue. I am working on authoring questions that use the algebra of functions (and later composition of functions). I currently am not as concerned about students simplifying (though I may change on that), but I want the answers that they see to be the simplified version.

For instance, perhaps I am adding/subtracting/dividing/multiplying rational functions. Is there a way to define the functions (I am currently using formula), say as f and g, and then do f+g simplified.

Ideally this would also work for cases where there is no reasonable simplification as well like adding a polynomial and radical expression together.

What I have is included below. It accepts the simplified and unsimplified version (as they are equivalent formulas).

Thank you!

DOCUMENT();

loadMacros(

"PGstandard.pl", # Standard macros for PG language

"MathObjects.pl",

"PGML.pl",

"contextLimitedPolynomial.pl",

);

# Print problem number and point value (weight) for the problem

TEXT(beginproblem());

# Show which answers are correct and which ones are incorrect

$showPartialCorrectAnswers = 1;

######

Context("Numeric");

Context()->noreduce('(-x)-y','(-x)+y');

$f = Formula("3/(x^2 -x -2)")->reduce;

$g = Formula("-5/(x^2 -4)")->reduce;

$fPlusg = Formula("$f+$g")->reduce;

$gMinusf = Formula("$g-$f")->reduce;

$fTimesg = Formula("$f*$g")->reduce;

$fByg = Formula("$f/$g")->reduce;

##############################################################

BEGIN_PGML

Consider [` f(x) = [$f] `] and [` g(x) = [$g] `].

a. What is the sum of [`f(x)`] and [`g(x)`]?

[`(f+g)(x) = `][_____________________________]{$fPlusg}

b. What is the difference of [`f(x)`] from [`g(x)`]?

[`(g-f)(x) = `][_____________________________]{$gMinusf}

c. What is the product of [`f(x)`] and [`g(x)`]?

[`(fg)(x) = `][_____________________________]{$fTimesg}

d. What is the quotient of [`f(x)`] by [`g(x)`]?

[`\left(\dfrac{f}{g}\right)(x) = `][_____________________________]{$fByg}

END_PGML

ENDDOCUMENT();