Is (x^2-1)/x^2 More Simplified Than 1-(1/x^2)?

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Homework Help Overview

The discussion revolves around the simplification of the expression (x^2-1)/x^2 compared to 1-(1/x^2) in the context of a calculus test question. Participants are exploring whether one form is officially considered more simplified than the other, particularly in relation to grading practices and the implications for students' marks.

Discussion Character

  • Conceptual clarification, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants are questioning the fairness of grading based on the perceived simplification of expressions. Some argue that both forms have their merits, while others suggest that combining fractions is a standard practice that should be followed. There is also discussion about the implications of simplification on further calculations, such as taking derivatives.

Discussion Status

The discussion is ongoing, with participants expressing differing opinions on the teacher's grading criteria. Some have provided insights into their own experiences with similar situations, while others are seeking further clarification on the rules governing simplification in mathematics. There is no explicit consensus, but several participants are advocating for a reconsideration of the grading decision.

Contextual Notes

Participants note that there may be a lack of clear guidelines regarding what constitutes a simplified expression in this context. The original poster expresses frustration over the impact of this grading decision on their overall mark, indicating that the issue is significant to them.

datdere
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I don't know if this is calculus or not but this was on a calculus test. It was the last step of a third derivative question. I lost a mark because the teacher says (x^2-1)/x^2 is more simplified than 1-(1/x^2).. is this fair? Is there an official rule that states (x^2-1)/x^2 is more simplified? Normally I wouldn't care about one mark but I was getting 100 in the course and that section was only out of 8 so now my mark is going to plummet for no reason.. -_-
 
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I take off points for my students if they don't combine fractions like this, and they also complain. Fair? That is in the eye of the beholder. Usually when you combine fractions by putting them over a common denominator, the numerator simplifies quite a bit. For example, sqrt(1/16 + 1/9) reduces to 5/12.
 
Well it is more simplified because you have to simplify it by finding the common denominator, therefore your teacher is correct. By the way it's nothing serious so don't be hard on yourself.
 
technicality. no way to get out of it. file it under 'syntax deduction'. perhaps attention to detail is required but not always necessary.
 
datdere said:
I don't know if this is calculus or not but this was on a calculus test. It was the last step of a third derivative question. I lost a mark because the teacher says (x^2-1)/x^2 is more simplified than 1-(1/x^2).. is this fair? Is there an official rule that states (x^2-1)/x^2 is more simplified? Normally I wouldn't care about one mark but I was getting 100 in the course and that section was only out of 8 so now my mark is going to plummet for no reason.. -_-

IMO, and having worked as a college math teacher for 19 years, I would say that the teacher is being pedantic and arbitrary in saying that his/her form is simpler than yours. Arguments could be made for either form being advantageous, but if you had to take one more derivative (the 4th), your form would be much simpler to work with. I'm assuming that the problem instructions didn't specify the form in which the answer should appear. If there were no such instructions, I don't understand why your teacher felt the need to deduct a point.
 
chrisbaird said:
I take off points for my students if they don't combine fractions like this, and they also complain. Fair? That is in the eye of the beholder. Usually when you combine fractions by putting them over a common denominator, the numerator simplifies quite a bit. For example, sqrt(1/16 + 1/9) reduces to 5/12.

you forgot the part where the fraction here DOESNT become simplified when you combine the fraction.. in fact it becomes complified therefore i don't see a reason to do this. there was another question where taking the common denom canceled out some stuff but here it did nothing so i didn't do it..
 
Mark44 said:
IMO, and having worked as a college math teacher for 19 years, I would say that the teacher is being pedantic and arbitrary in saying that his/her form is simpler than yours. Arguments could be made for either form being advantageous, but if you had to take one more derivative (the 4th), your form would be much simpler to work with. I'm assuming that the problem instructions didn't specify the form in which the answer should appear. If there were no such instructions, I don't understand why your teacher felt the need to deduct a point.

Exactly right. I don't agree with the teacher.

For that matter, what if I'd "simplified" the expression further by a needless factorisation to (x+1)(x-1)/x^2? Would I get extra credit? :rolleyes:
 
Curious3141 said:
Exactly right. I don't agree with the teacher.

For that matter, what if I'd "simplified" the expression further by a needless factorisation to (x+1)(x-1)/x^2? Would I get extra credit? :rolleyes:

Thanks for the replies, any more thoughts so I can show him this thread? If there's no official rule about making a common denominator I'm going to talk to her about this again (I tried once already T.T).

The only solid thing I can say is that taking the derivative of my form is easier, and since he said always use a simplified form before taking the next derivative, his argument is in my favour, lol

Honestly if there's no written rules about this it doesn't make sense to take off a whole mark out of 3 -.-also want to add @chrisbaird, why are you taking marks off from your students when it's clearly a debatable topic? If you have students arguing about it, why are you taking off marks? I don't understand.
 
Last edited:
datdere said:
also want to add @chrisbaird, why are you taking marks off from your students when it's clearly a debatable topic? If you have students arguing about it, why are you taking off marks? I don't understand.

Your case does not seem as serious a mistake as others, but when you get into other topics such as infinite series expansions, taking this step becomes crucial.
 

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