Divide 3n^2-n/n^2-1/n^2/n+1
To simplify the given expression, we have:
(3n^2 - n) / ((n^2 - 1) / (n^2 / (n + 1)))
We can start by simplifying the denominator's denominator, which is n^2 / (n + 1). This can be rewritten as (n^2 * 1 / (n + 1)).
The expression now becomes:
(3n^2 - n) / ((n^2 - 1) / (n^2 * 1 / (n + 1)))
Next, we can simplify the numerator by factoring out the common term:
n(3n - 1)
The expression becomes:
(n(3n - 1)) / ((n^2 - 1) / (n^2 * 1 / (n + 1)))
Now, let's simplify the denominator by factoring it:
(n^2 - 1)
This is a difference of squares, which can be factored into:
(n + 1)(n - 1)
Since the denominator (n^2 - 1) is being divided by the entire expression (n^2 * 1 / (n + 1)), it becomes the numerator of the whole expression:
(n(3n - 1)) / ((n + 1)(n - 1))
So, the simplified form of the given expression is:
(n(3n - 1)) / ((n + 1)(n - 1)).