Question

Alguém me explica como fazer (n+4)!/(n+2)!+(n+3)!

Answer 1

Temos um caso de fatorial, e para resolver, tentamos reduzir a fim de anular os iguais.... Sabemos que:

$(n+4)!=(n+4)(n+3)(n+2)!\\\\ (n+3)!=(n+3)(n+2)!$

$\frac{(n+4)!}{(n+2)!+(n+3)!}\\\\ \frac{(n+4)(n+3)(n+2)!}{(n+2)!+(n+3)(n+2)!}\\\\ \frac{(n+4)(n+3)(n+2)!}{(n+2)!(1+n+3)}\\\\ \frac{(n+4)(n+3)(n+2)!}{(n+4)(n+2)!}\\\\ \boxed{(n+3)}$