I'm re-learning factorials, and I encountered this exercice, but the solution had a diferent result than I got, and no matter how much I try to search, I can't find an explanation to the last step of this:
$\frac{100!+98!}{100!-98!}\iff\frac{(100\times 99\times 98!)+98!}{(100\times 99\times 98!)-98!}\iff\frac{98!(9900+1)}{98!(9900-1)}\iff\frac{9901}{9899}$
I understand $100 \times 99 = 9900$ but where does the $1$ come from? and where does the $98!$ go?
Can someone please explain me that last step?
When I calculated myself I simply canceled and got:
$\frac{100 \times 99 \times 98! + 98!}{100 \times 99 \times 98! - 98!} = \frac{98!}{98!} = 1$
Where am I going wrong? Thanks,