# PartFrac: Answer test results

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
Teacher answer
Opt
Mark
Answer note
PartFrac
1/0
3*x^2
-1 STACKERROR_OPTION.
TEST_FAILED
The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test.
PartFrac
1/0
3*x^2
x
-1 ATPartFrac_STACKERROR_SAns.
TEST_FAILED
The answer test failed to execute correctly: please alert your teacher. Division by zero.
PartFrac
0
0
1/0
-1 ATPartFrac_STACKERROR_Opt.
TEST_FAILED
The answer test failed to execute correctly: please alert your teacher. Division by zero.
PartFrac
0
1/0
x
-1 ATPartFrac_STACKERROR_TAns.
TEST_FAILED
The answer test failed to execute correctly: please alert your teacher. Division by zero.
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.
The answer test failed. Please contact your systems administrator
Basic tests
PartFrac
1/m
1/n
n
0 ATPartFrac_diff_variables.
The variables in your answer are different to those of the question, please check them.
PartFrac
2/(x+1)-1/(x+2)
s/((s+1)*(s+2))
s
0 ATPartFrac_diff_variables.
The variables in your answer are different to those of the question, please check them.
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.
Addition and Subtraction errors
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.
Irreducible quadratic in denominator
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.
Correct Answer, Numerator > Denominator
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.