I have a question. I am new here so I am sorry if this question is bad or vague. I'm having some issues solving this one factorial question: shown below:
$8! -7 * 7! + 6 * 6! \over 7!-6*6!+5*5!$
I know the answer is $78/11$. I don't understand the way to solve this though. The solution said to split $8!$ into $8 * 7 * 6!$ and $7!$ into $7 * 6!$ for the numbers in the numerator. Then you get $8 * 7 -7 * 7 + 6 * 6!$. I know that they removed the $6!$ from the numerator and multiplied the $6!$ to $13$ which is the simplified expression $8 * 7 -7 * 7 + 6$. The part I don't understand is why they did that. In the original equation, there are 3 $6!$ (in the numerator's original equation). Why do they multiply $6!$? Thanks in advance.