Răspuns:
n = -1/3 sau n = 2
Explicație pas cu pas:
n! inseamna 1 * 2 * 3*...*(n-1)*n, asadar:
[tex]\frac{(n-1)!}{n!(n+2)} + \frac{3}{n+1} = \frac{9}{2(n+2)}\\\\\frac{1}{n(n+2)} + \frac{3}{n+1} = \frac{9}{2(n+2)} | *2n(n+1)(n+2)\\\\2(n+1) + 3*2n(n+2) = 9n(n+1)\\2n + 2 + 6n^{2} + 12n = 9n^{2} + 9n\\-3n^{2} + 5n + 2 = 0[/tex]
Rezolvand ecuatia de gradul 2, obtinem n = -1/3 sau n = 2
