# Not only AM-GM 3 (The Other AM-GM Part 5)

Algebra Level 4

Find the minimum value of the expression below, for real $a,b,c,d,e >0$

\begin{aligned} \dfrac{b+c+d+e}{a} + \dfrac{a+c+d+e}{b} + \dfrac{a+b+d+e}{c} + \dfrac{a+b+c+e}{d} + \dfrac{a+b+c+d}{e} \end{aligned}

Bonus: For real $x_1 , x_2 , x_3 , x_4 , \cdots , x_n >0$, let $x_1 + x_2 + x_3 + x_4 + \cdots + x_n = S$. Find the minimum value of $\dfrac{S- x_1}{x_1} + \dfrac{S-x_2}{x_2} + \dfrac{S-x_3}{x_3} + \cdots + \dfrac{S-x_n}{x_n}$ in term of $n$.