This page exposes the results of running answer tests on STACK test cases. This page is automatically generated from the STACK unit tests and is designed to show question authors what answer tests actually do. This includes cases where answer tests currentl fail, which gives a negative expected mark. Comments and further test cases are very welcome.

## PartFrac

Test
?
Student response
Opt
Mark
PartFrac
1/0
3*x^2
-1 STACKERROR_OPTION.
TEST_FAILED
PartFrac
1/0
3*x^2
x
-1 ATPartFrac_STACKERROR_SAns.
TEST_FAILED
PartFrac
0
0
1/0
-1 ATPartFrac_STACKERROR_Opt.
TEST_FAILED
PartFrac
0
1/0
x
-1 ATPartFrac_STACKERROR_TAns.
TEST_FAILED
PartFrac
1/n=0
1/n
n
0 ATPartFrac_SA_not_expression.
Your answer should be an expression, not an equation, inequality, list, set or matrix.
PartFrac
1/n
{1/n}
n
0 ATPartFrac_TA_not_expression.
Basic tests
PartFrac
1/m
1/n
n
0 ATPartFrac_diff_variables.
PartFrac
2/(x+1)-1/(x+2)
s/((s+1)*(s+2))
s
0 ATPartFrac_diff_variables.
PartFrac
1/n
1/n
n
1 ATPartFrac_true.
PartFrac
n^3/(n-1)
n^3/(n-1)
n
0 ATPartFrac_false_factor.
PartFrac
1+n+n^2+1/(n-1)
n^3/(n-1)
n
1 ATPartFrac_true.
PartFrac
1+n+n^2-1/(1-n)
n^3/(n-1)
n
1 ATPartFrac_true.
Distinct linear factors in denominator
PartFrac
1/(n+1)-1/n
1/(n+1)-1/n
n
1 ATPartFrac_true.
PartFrac
1/(n+1)+1/(1-n)
1/(n+1)-1/(n-1)
n
1 ATPartFrac_true.
PartFrac
1/(2*(n-1))-1/(2*(n+1))
1/((n-1)*(n+1))
n
1 ATPartFrac_true.
PartFrac
1/(2*(n+1))-1/(2*(n-1))
1/((n-1)*(n+1))
n
0 ATPartFrac_ret_expression.
Your answer as a single fraction is $$-\frac{1}{\left(n-1\right)\cdot \left(n+1\right)}$$
PartFrac
-9/(x-2) + -9/(x+1)
-9/(x-2) + -9/(x+1)
x
1 ATPartFrac_true.
PartFrac
1/(x+1) + 1/(x+2)
2/(x+1) + 1/(x+2)
x
0 ATPartFrac_ret_expression.
Your answer as a single fraction is $$\frac{2\cdot x+3}{\left(x+1\right)\cdot \left(x+2\right)}$$
PartFrac
1/(x+1) + 1/(x+2)
1/(x+1) + 2/(x+2)
x
0 ATPartFrac_ret_expression.
Your answer as a single fraction is $$\frac{2\cdot x+3}{\left(x+1\right)\cdot \left(x+2\right)}$$
Denominator Error
PartFrac
1/(x+1) + 1/(x+2)
1/(x+3) + 1/(x+2)
x
0 ATPartFrac_ret_expression.
Your answer as a single fraction is $$\frac{2\cdot x+3}{\left(x+1\right)\cdot \left(x+2\right)}$$
Repeated linear factors in denominator
PartFrac
(9*y-8)/(y-4)^2
(9*y-8)/(y-4)^2
y
0 ATPartFrac_false_factor.
PartFrac
9/(y-4)+28/(y-4)^2
(9*y-8)/(y-4)^2
y
1 ATPartFrac_true.
PartFrac
(-5/(x+3))+(16/(x+3)^2)-(2/(x+
2))+4
(-5/(x+3))+(16/(x+3)^2)-(2/(x+
2))+4
x
1 ATPartFrac_true.
PartFrac
(3*x^2-5)/((x-4)^2*x)
(3*x^2-5)/((x-4)^2*x)
x
0 ATPartFrac_false_factor.
PartFrac
-4/(16*x)+53/(16*(x-4))+43/(4*
(x-4)^2)
(3*x^2-5)/((x-4)^2*x)
x
0 ATPartFrac_ret_expression.
Your answer as a single fraction is $$\frac{49\cdot x^2-8\cdot x-64}{16\cdot {\left(x-4\right)}^2\cdot x}$$
PartFrac
-5/(16*x)+53/(16*(x-4))+43/(4*
(x-4)^2)
(3*x^2-5)/((x-4)^2*x)
x
1 ATPartFrac_true.
PartFrac
(5*x+6)/((x+1)*(x+5)^2)
(5*x+6)/((x+1)*(x+5)^2)
x
0 ATPartFrac_false_factor.
PartFrac
-1/(16*(x+5))+19/(4*(x+5)^2)+1
/(16*(x+1))
(5*x+6)/((x+1)*(x+5)^2)
x
1 ATPartFrac_true.
PartFrac
5/(x*(x+3)*(5*x-2))
5/(x*(x+3)*(5*x-2))
x
0 ATPartFrac_false_factor.
PartFrac
125/(34*(5*x-2))+5/(51*(x+3))-
5/(6*x)
5/(x*(x+3)*(5*x-2))
x
1 ATPartFrac_true.
PartFrac
-4/(16*x)+1/(2*(x-1))-1/(8*(x-
1)^2)
(3*x^2-5)/((4*x-4)^2*x)
x
0 ATPartFrac_ret_expression.
Your answer as a single fraction is $$\frac{2\cdot x^2-x-2}{8\cdot {\left(x-1\right)}^2\cdot x}$$
PartFrac
-5/(16*x)+1/(2*(x-1))-1/(8*(x-
1)^2)
(3*x^2-5)/((4*x-4)^2*x)
x
1 ATPartFrac_true.
PartFrac
1/(x-1)-(x+1)/(x^2+1)
2/((x-1)*(x^2+1))
x
1 ATPartFrac_true.
PartFrac
1/(2*x-2)-(x+1)/(2*(x^2+1))
1/((x-1)*(x^2+1))
x
1 ATPartFrac_true.
PartFrac
1/(2*(x-1))+x/(2*(x^2+1))
1/((x-1)*(x^2+1))
x
0 ATPartFrac_ret_expression.
Your answer as a single fraction is $$\frac{2\cdot x^2-x+1}{2\cdot \left(x-1\right)\cdot \left(x^2+1 \right)}$$
PartFrac
(2*x+1)/(x^2+1)-2/(x-1)
(2*x+1)/(x^2+1)-2/(x-1)
x
1 ATPartFrac_true.
2 answers to the same question
PartFrac
3/(x+1) + 3/(x+2)
3*(2*x+3)/((x+1)*(x+2))
x
1 ATPartFrac_true.
PartFrac
3*(1/(x+1) + 1/(x+2))
3*(2*x+3)/((x+1)*(x+2))
x
1 ATPartFrac_true.
Algebraically equivalent, but numerators of same order than denominator, i.e. not in partial fraction form.
PartFrac
3*x*(1/(x+1) + 2/(x+2))
-12/(x+2)-3/(x+1)+9
x
0 ATPartFrac_false_factor.
PartFrac
(3*x+3)*(1/(x+1) + 2/(x+2))
9-6/(x+2)
x
0 ATPartFrac_false_factor.
PartFrac
n/(2*n-1)-(n+1)/(2*n+1)
1/(4*n-2)-1/(4*n+2)
n
0 ATPartFrac_false_factor.
PartFrac
10/(x+3) - 2/(x+2) + x -2
(x^3 + 3*x^2 + 4*x +2)/((x+2)*
(x+3))
x
1 ATPartFrac_true.
PartFrac
2*x+1/(x+1)+1/(x-1)
2*x^3/(x^2-1)
x
1 ATPartFrac_true.
Simple mistakes
PartFrac
1/(n*(n-1))
1/(n*(n-1))
n
0 ATPartFrac_false_factor.
PartFrac
((1-x)^4*x^4)/(x^2+1)
((1-x)^4*x^4)/(x^2+1)
x
0 ATPartFrac_false_factor.
PartFrac
1/(n-1)-1/n^2
1/((n+1)*n)
n
0 ATPartFrac_denom_ret.
If your answer is written as a single fraction then the denominator would be $$\left(n-1\right)\cdot n^2$$. In fact, it should be $$n\cdot \left(n+1\right)$$.
PartFrac
1/(n-1)-1/n
1/(n-1)+1/n
n
0 ATPartFrac_ret_expression.
Your answer as a single fraction is $$\frac{1}{\left(n-1\right)\cdot n}$$
PartFrac
1/(x+1)-1/x
1/(x-1)+1/x
x
0 ATPartFrac_ret_expression.
Your answer as a single fraction is $$-\frac{1}{x\cdot \left(x+1\right)}$$
PartFrac
1/(n*(n+1))+1/n
2/n-1/(n+1)
n
0 ATPartFrac_false_factor.
Too many parts in the partial fraction
PartFrac
s/((s+1)^2) + s/(s+2) - 1/(s+1
)
s/((s+1)*(s+2))
s
0 ATPartFrac_denom_ret.
If your answer is written as a single fraction then the denominator would be $${\left(s+1\right)}^2\cdot \left(s+2\right)$$. In fact, it should be $$\left(s+1\right)\cdot \left(s+2\right)$$.
Too few parts in the partial fraction
PartFrac
s/(s+2) - 1/(s+1)
s/((s+1)*(s+2)*(s+3))
s
0 ATPartFrac_denom_ret.
If your answer is written as a single fraction then the denominator would be $$\left(s+1\right)\cdot \left(s+2\right)$$. In fact, it should be $$\left(s+1\right)\cdot \left(s+2\right)\cdot \left(s+3\right)$$.
PartFrac
(3*x^2-5)/((4*x-4)^2*x)
(3*x^2-5)/((4*x-4)^2*x)
x
0 ATPartFrac_false_factor.