Need some help with an exponent simplification questions

[i-love-physics]

Homework Statement

express the given expression in simplest form with only possitive exponents

Homework Equations

**refer to attached drawing**

The Attempt at a Solution

Refer to attached drawing to see my attempt and to see what the real answer is. I don't understand where i went wrong in my steps, in the final answer there is a (-4n) i don't know where that came from.

Greatly appreciated if one of you smart guys could lend us a hand. Thank you.

 

[HallsofIvy]

you have
$$\left(\frac{1}{n}- \frac{2}{n}\right)^2$$
and say that is equal to
$$\left(\frac{n-2n^2}{n^3}\right)^2$$
While they are equal, the LEAST common denominator is n², not n³. You do, in fact, eventually cancel the spare "n"s so that is not the problem.

The real problem is that you have
$$\left(\frac{n- 2n^2}{n^3}\right)^2$$
and say that is equal to
$$\frac{n^2- 4n^4}{n^6}$$
That is incorrect: (a- b)² is NOT a²- b²!
It is a²- 2ab+ b². You forgot the "middle term".

 

[i-love-physics]

thanks

Thanks a lot HallsofIvy, i appreciate your help mate.

It was such an obvious solution i can't believe i didnt figure it out myself.

Why does this happen sometimes?, the answer is right in front of you but a person still fails to see it?

I think i must be tired from work that is why. Or mybe i am craming in too much maths information into my brain in such a short period of time.

Anyway...thanks again.