The evaluation type eval rational function can be used to check (multivariate) rational functions. It does not have automated feedback itself, but instead the evaluation type fb rational function can be used to give automated (positive or negative) feedback on the student’s answer.

The Definition field of this evaluation type should have a (multivariate) rational function.

Example:

When this evaluation type is used in a Solution rule, the evaluation type fb rational function can be used in positive or negative feedback to give automated feedback on the student’s answer.

**Evaluation type: fb rational function**

This evaluation type can only be used in (positive and negative) feedback when a solution rule is defined that uses eval rational function. The Definition field should contain the name of the desired form of the rational function. The possible forms are:

`basic`

Use this if the student’s rational function can only contain the operators plus, minus, times, divide, and power (but only to integer exponents) and there are no further restrictions on the form of the rational function.

`combined`

Use this if the student’s rational function should be a quotient of two polynomials P and Q, so P/Q, such that P and Q are coprime.

`quotient`

Use this if the student’s rational function should be a quotient of two expanded polynomials P and Q, so P/Q, where P and Q are not necessarily coprime.

`split`

Use this if the student’s rational function should be a sum of quotients with irreducible denominators. The student’s answer should be of the form:

**Examples of feedback**

Examples of automated feedback that is given by fb rational function (depending on the form that you choose) are:

You are missing variable x in your answer / Variable z does not belong in your answer.

You divide by zero in your answer.

You can decrease the degree of the numerator and denominator.

You can combine some terms.

Expand the brackets.

The degree of the numerator/denominator is not correct.

There is a term missing in your answer.

Your answer is not the quotient of two polynomials.

According to your answer, the value of the function at x=1 is ⅓, but it should be ⅔.

etc.

Some concrete examples are given below. The solution rule that is used for these examples is:

Example 1 (`basic`

, negative feedback):

Example 2 (`combined`

, positive feedback):