## PREP 2015 Question Authoring - Archived

### Context()->texStrings and contextFraction still producing algebra strings

by tim Payer -
Number of replies: 0
Hello

I am still having a bit of difficulty getting "pretty" fractions to present in solutions:

I thought that the essential commands to make this happen were:
1.) Load the macro: "contextFraction.pl"
2.) initialize before the fraction variable is declared:  Context("Fraction");
3.) Use this before said variable: Context()->texStrings;
4.) Use this after said variable: Context()->normalStrings;

Unfortunately the fractions are coming out in algebra strings wrapped in parentheses: (5/6)  rather than the pretty tex style.

Can you see my error?

Thanks so much...

## DESCRIPTION
## Calculus
## ENDDESCRIPTION

## Tagged by tda2d

## DBsubject(Calculus - single variable)
## DBchapter(Differentiation)
## DBsection(Quotient rule (without trigonometric functions))
## Institution(ASU)
## Level(3)
## KEYWORDS('Differentiation' 'Product Rule' 'Quotient Rule')
## MO(1)
## updated 12/2014
## updated 8/2015 with solutions, Original path:
## Library/ASU-topics/setProductQuotientRule/3-5-51

DOCUMENT();

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"contextFraction.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
);

TEXT(beginproblem());
$showpartialcorrectanswers = 1; Context("Numeric");$a = random(2, 4, 1);
$b = random(3, 8,1);$c = random(2,7,1);
$d = random(3,9,1);$f = random(2,6,1);
$g = random(4, 12, 1);$ah = $a*0.5;$d2 = $d*2;$ahd = $ah*$d;
$ahf =$ah*$f;$ahg = $ah*$g;
$ad2 =$a*$d2;$af = $a*$f;
$ta =$ahd - $ad2;$tb = $ahf -$af;
$r1 = random(1,5,1);$tar = $ta*$r1;
$rsq =$r1*$r1;$fr = $f*$r1;
$drsq =$d*$rsq;$frg = $fr -$g;
$tarb =$tar +$tb;$den1 =$drsq+$frg;
$den2 =$den1**2;
$tarbr =$tarb*$r1;$tarb2 = $tarbr -$ahg;

Context("Fraction");
Context()->texStrings;
$frac1 = Fraction("$tarb2/$den2"); Context()->normalStrings;$r2 = random(-7,-1,1);
$h1 =$a*(($r1)**(.5));$dh1 = ($a/2)*(($r1)**(-.5));
$l1 =$d*(($r1)**2) +$f*($r1) -$g;
while ($d*(($r1)**2) + $f*($r1) - $g == 0) {$g = random(4, 12, 1);
$l1 =$d*(($r1)**2) +$f*($r1) -$g;
}
$dl1 = 2*$d*$r1 +$f;

BEGIN_TEXT
Let
$f(x) = \frac{a \sqrt{x} }{d x^2 + f x - g}.$
Evaluate $$f'(x)$$ at $$x = r1$$.
$BR$BR
$$f'(r1)$$ = \{ans_rule(50) \}
END_TEXT

$ans = Compute("(($l1)*($dh1) - ($h1)*($dl1))/(($l1)**2)");
ANS($ans->cmp); #ANS(num_cmp($ans));

SOLUTION(EV3(<<'END_SOLUTION'));
$PAR SOLUTION$PAR

Use the quotient rule to find the derivative of a quotient:$BR If $$Q(x) = \frac{N(x)}{D(x)}$$, then the derivative of Q(x) can be expressed as$BR
$BR $$Q'(x) = \frac{N'(x) \cdot D(x) - N(x) \cdot D'(x)}{(D(x))^2}$$.$BR
$BR Convert the root to a rational exponent.$BR
$BR $$\displaystyle{f(x) = \frac{a x^{\frac{1}{2}} }{d x^2 + f x - g}}$$$BR
$BR Apply the prime tics for the quotient rule and square the denominator.$BR
$BR $$\displaystyle{f'(x) = \frac{a \left(x^{\frac{1}{2}}\right)'(d x^2 + f x - g) - a x^{\frac{1}{2}}(d x^2 + f x - g)' }{(d x^2 + f x - g)^2}}$$$BR
$BR Apply the derivative.$BR
$BR $$\displaystyle{f'(x) = \frac{ah x^{\frac{-1}{2}}(d x^2 + f x - g) - a x^{\frac{1}{2}}(d2 x + f - 0) }{(d x^2 + f x - g)^2}}$$$BR
$BR Distribute through the numerator.$BR
$BR $$\displaystyle{f'(x) = \frac{ahd x^{\frac{3}{2}} +ahf x^{\frac{1}{2}} -ahg x^{\frac{-1}{2}} - ad2 x^{\frac{3}{2}}- af x^{\frac{1}{2}}}{(d x^2 + f x - g)^2}}$$$BR
$BR Collect like terms.$BR
$BR $$\displaystyle{f'(x) = \frac{(ahd -ad2)x^{\frac{3}{2}} +(ahf -af) x^{\frac{1}{2}} -ahg x^{\frac{-1}{2}} }{(d x^2 + f x - g)^2}}$$$BR
$BR Reduce and the result is the derivative.$BR
$BR $$\displaystyle{f'(x) = \frac{ta x^{\frac{3}{2}} +tb x^{\frac{1}{2}} -ahg x^{\frac{-1}{2}} }{(d x^2 + f x - g)^2}}$$$BR
$BR Evaluate the derivative at x =$r1. $BR$BR
$$\displaystyle{f'(r1) = \frac{ta \cdot r1^{\frac{3}{2}} +tb \cdot r1^{\frac{1}{2}} -ahg \cdot r1^{\frac{-1}{2}} }{(d \cdot r1^2 + f \cdot r1 - g)^2}}$$$BR$BR
$BR Reduce the \frac{3}{2} root, and combine denominator factors:$BR
$BR $$\displaystyle{f'(r1) = \frac{ta \cdot r1\cdot r1^{\frac{1}{2}} +tb \cdot r1^{\frac{1}{2}} -ahg \cdot r1^{\frac{-1}{2}} }{(d \cdot rsq + fr - g)^2}}$$$BR
$BR$BR
Convert rational exponents to roots, and convert the negative root to a positive root by a denominator placement:
$$\displaystyle{f'(r1) = \frac{(tar +tb) \sqrt{r1} -\frac{ahg}{\sqrt{r1}} }{(drsq + frg)^2}}$$$BR$BR

$BR Combine constants:$BR
$$\displaystyle{f'(r1) = \frac{tarb \sqrt{r1} -\frac{ahg}{\sqrt{r1}} }{den1^2}}$$$BR$BR
$BR Multiply each term by \sqrt{$r1}. $BR$BR
$$\displaystyle{f'(r1) = \frac{tarb \sqrt{r1} \cdot \sqrt{r1} -\frac{ahg \cdot \sqrt{r1}}{\sqrt{r1}} }{\sqrt{r1} \cdot den2}}$$$BR$BR
Reduce root factors. $BR$BR
$$\displaystyle{f'(r1) = \frac{tarb \cdot r1 -ahg }{\sqrt{r1} \cdot den2}}$$$BR$BR
$BR Combine factors.$BR
$BR $$\displaystyle{f'(r1) = \frac{tarbr -ahg }{\sqrt{r1} \cdot den2}}$$$BR
$BR Combine terms and separate the root.$BR
$BR $$\displaystyle{f'(r1) = \frac{tarb2}{ den2}\cdot \frac{1}{\sqrt{r1}}}$$$BR
$BR$BR
Reduce. $BR $$\displaystyle{f'(r1) = frac1 \cdot \frac{1}{\sqrt{r1}}}$$$BR
\$BR
END_SOLUTION

ENDDOCUMENT();