Question

n!+(n+1)!
_______
n!

Answer 1

$\dfrac{n!+\left(n+1 \right )!}{n!}\\ \\ =\dfrac{n!+ \left(n+1 \right )\cdot n!}{n!}\\ \\ =\dfrac{1\cdot n!+ \left(n+1 \right )\cdot n!}{n!}$


Colocando $n!$ em evidência, temos

$=\dfrac{n!\cdot \left[1+\left(n+1 \right ) \right ]}{n!}\\ \\ =\dfrac{\diagup\!\!\!\!\! n!\cdot \left[n+2 \right ]}{\diagup\!\!\!\!\! n!}\\ \\ =n+2$