Divide 3n^2-n/n^2-1/n^2/n+1
To divide the expression (3n^2-n)/(n^2-1)/(n^2/n+1), we can simplify it step by step.
Step 1: Simplify the expression within the parentheses.
The expression within the parentheses is (3n^2-n)/(n^2-1).
Step 2: Simplify the fractions separately.
To simplify the fractions, we need to find the common denominator. The common denominator is n^2.
For the first fraction (3n^2-n), multiply the numerator and denominator by n+1 to eliminate the denominator n^2-1:
[(3n^2-n)(n+1)] / [(n^2-1)(n+1)]
For the second fraction (n^2/n+1), multiply the numerator and denominator by n^2-1 to eliminate the denominator n+1:
[(n^2)(n^2-1)] / [(n+1)(n^2-1)]
Step 3: Simplify further.
Now that we have a common denominator, we can combine the fractions by adding or subtracting the numerators:
[(3n^3 + 3n^2 - n - n^2)] / [(n^3 + n^2 - n - 1)(n^2-1)]
Simplifying the numerator gives us:
[3n^3 + 2n^2 - n] / [(n^3 + n^2 - n - 1)(n^2-1)]
And simplifying the denominator gives us:
[(n)(n+1)(n-1)(n^2-1)]
Step 4: Cancel out common factors.
We can now cancel out common factors in the numerator and denominator:
[3n(n^2 + 2n - 1)] / [(n)(n+1)(n-1)(n+1)(n-1)]
Step 5: Simplify the expression further.
Simplifying the expression, we get:
[3n(n^2 + 2n - 1)] / [(n)(n+1)(n-1)^2]
This is the simplified form of the given expression (3n^2-n)/(n^2-1)/(n^2/n+1).