Question

Resolva o fatorial (n+3)!(n-1)!/(n-2)!(n+4)! = 1346

Answer 1

(n+3)!(n-1).(n-2)!/(n-2)!(n+4).(n+3)!=1346 corta (n-2)! com (n-2)! e (n+3)! com (n+3)!

Fica assim:

(n-1)/(n+4)=1346 faz meio pelos extremos:

n-1=1346n+5384

1345n=5385
n=5385/1345
n=4,0029

Answer 2

            $\frac{(n + 3)!(n - 1)!}{(n - 2)!(n + 4)!} = 1346 \\ \\ \frac{(n+3)!(n-1)(n-2)!}{(n-2)!(n+4)(n+3)!}=1346 \\ \\ \frac{n-1}{n+4} =1346 \\ \\ n-1=1346.(n+4) \\ \\ n-1=1346n +5384 \\ \\ n-1346n=5384+1 \\ \\ -1345n=5385$
 
            $n=- \frac{5385}{1345} \\ \\ n=- \frac{1077}{269}$