Divide 3n^2-n/n^2-1/n^2/n+1

You are unlikely to get a reply if you are not clear about what are the various numerators and denominators. Do you mean what you typed or:

(3n^2-n)/(n^2-1)/(n^2)/(n+1 )

If it is as I typed it:

[ (3n^2-n)/(n^2-1) ]/ [(n^2)/(n+1 ) ]

[ (3n^2-n)/{n+1)(n-1) } ]/ [(n^2)/(n+1 ) ]

[ (3n^2-n)/(n-1) } ]/ [(n^2)/ ]

[ (3n^2-n)/(n-1) } ]/ [(n^2)/ ]

[ (3n-1)/(n-1) } ]/ [(n) ]

(3n-1) / (n^2-n)

To divide the given expression, we can simplify it step by step. Let's break down the expression into smaller parts:

First, let's simplify the numerator, which is 3n^2 - n:
Since there is no common factor in the terms, we cannot factorize it further.

Next, let's simplify the denominator, which is n^2 - 1:
It can be factored as a difference of squares: (n + 1)(n - 1).

Now, let's simplify the denominator of the whole expression, which is n^2:
There is no further simplification possible for n^2.

Finally, let's simplify the whole expression by dividing:
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. Therefore, we multiply the numerator by the reciprocal of the denominator.

Thus, the given expression can be simplified as follows:

(3n^2 - n) / (n^2 - 1) / (n^2 / n + 1)
= (3n^2 - n) / (n^2 - 1) * ((n + 1)(n - 1) / (n^2))
= (3n^2 - n) / ((n + 1)(n - 1)) * (n^2 / n^2)
= (3n^2 - n) / ((n + 1)(n - 1)) * 1
= (3n^2 - n) / ((n + 1)(n - 1))
= (n(3n - 1)) / ((n + 1)(n - 1))

Therefore, the simplified form of the given expression is (n(3n - 1)) / ((n + 1)(n - 1)).