Question

simplifique, ao máximo possível a expressão: m! + (m-1)! / (m+1)! - m!

Answer 1

$\frac{m!+(m-1)!}{(m+1)!-m!}=\\\\\\\frac{m\cdot(m-1)!+(m-1)!}{(m+1)\cdot\,m!-m!}=\\\\\\\frac{(m-1)!\left[m+1\right]}{m!\left[(m+1)-1\right]}=\\\\\\\frac{(m+1)(m-1)!}{m\cdot\,m!}=\\\\\\\frac{(m+1)(m-1)!}{m\cdot\,m(m-1)!}=\\\\\\\boxed{\frac{m+1}{m^2}}$