Perform and reduce?

Question

Perform indicated operation-reduce-show your work
4/3n + 2/n+1 + 2/n^2+n

4 + 2 + 2
3n n+1 n^2 + n

Answer 1

As written your probelm is:
4/3n + 2/n+1 + 2/n^2+n
7/3n + 1 + 2/n + 2/n²
(7/3n³+n²+2n+2)/n²

Which isn't particularly simple. But since I suspect you meant to write:
4/(3n) + 2/(n+1) + 2/(n^2+n)
You get:
4/(3n) + 2/(n+1) + 2/(n(n+1))
4(n+1)/(3n(n+1)) + 6n/(3n(n+1)) + 6/(3n(n+1))
(4(n+1) + 6n + 6)/(3n(n+1))
(4n+4+6n+6)/(3n(n+1))
(10n+10)/(3n(n+1))
(10(n+1))/(3n(n+1))
10/(3n)

Answer 2

(4/(3n)) + (2/(n + 1)) + (2/(n^2 + n))
(4/(3n)) + (2/(n + 1)) + (2/(n(n + 1)))

Multiply everything by (3n)(n + 1)

(4(n + 1) + 2(3n) + 2(3))/((3n)(n + 1))

(4n + 4 + 6n + 6)/((3n)(n + 1))

(10n + 10)/((3n)(n + 1))

(10(n + 1))/((3n)(n + 1))

ANS : 10/(3n) or (10/3)n^-1

Answer 3

Factor the n^2 + n; find the common denominator; multiply tops and bottoms by any factor missing from each bottom. Then combine like terms on top. factor this if possible. Cancel any common factors with the bottom.