Question

Помогите пожалуйста упростить! ((n^4 + n^3 + n^2 + n + 1)/(n^5 - 1)) - (n^2 - n + 1)/(n^3 + 1)

Answer 1

$frac{n^4+n^3+n^2+n+1}{n^5-1}-frac{n^2-n+1}{n^3+1}=\\ frac{n^4+n^3+n^2+n+1}{(n-1)(n^4+n^3+n^2+n+1)}-frac{n^2-n+1}{(n+1)(n^2-n+1)}= frac{1}{n-1}-frac{1}{n+1}=frac{1*(n+1)}{(n-1)*(n+1)}-frac{1*(n-1)}{(n+1)(n-1)}=\\ frac{n+1-(n-1)}{n^2-1}=frac{n+1-n+1}{n^2-1}=frac{2}{n^2-1}$