Question

Simplifique a expressão Cx + 1,3/Cx,2

Answer 1

$\frac{C_{x+1,3}}{C_{x,2}}~=~\frac{\frac{(x+1)!}{3!\,.\,(\,(x+1)-3\,)!}}{\frac{x!}{2!\,.\,(x-2)!}}\\\\\\\frac{C_{x+1,3}}{C_{x,2}}~=~\frac{(x+1)!}{3!\,.\,(\,(x+1)-3\,)!}~.~\frac{2!\,.\,(x-2)!}{x!}\\\\\\\frac{C_{x+1,3}}{C_{x,2}}~=~\frac{(x+1)!}{6\,.\,(x-2)!}~.~\frac{2\,.\,(x-2)!}{x!}\\\\\\\frac{C_{x+1,3}}{C_{x,2}}~=~\frac{(x+1)!\,.\,2\,.\,(x-2)!}{6\,.\,(x-2)!\,.\,x!}\\\\\\\frac{C_{x+1,3}}{C_{x,2}}~=~\frac{(x+1)!\,.\,2\,.\,1}{6\,.\,1\,.\,x!}$

$\frac{C_{x+1,3}}{C_{x,2}}~=~\frac{(x+1)!\,.\,1}{3\,.\,x!}\\\\\\\frac{C_{x+1,3}}{C_{x,2}}~=~\frac{(x+1).x!}{3\,.\,x!}\\\\\\\boxed{\frac{C_{x+1,3}}{C_{x,2}}~=~\frac{x+1}{3}}$