Question

Simplify:
[3(n+3)!]/5n!

Answer 1

there are no parentheses around the number right? it is
\[\frac{3(n+3)!}{5n!}\]

Answer 2

yup!

Answer 3

you distribute the 3 first I believe to get 3n +3!

Answer 4

@satellite73

Answer 5

oh hell no

Answer 6

for example
\[3\times 5!=3\times 5\times 4\times 3\times 2\times 1\]

Answer 7

don't distribute anything
leave the \(\frac{3}{5}\) out front

Answer 8

then
\[(n+3)!=(n+3)(n+2)(n+1)n!\] cancel the \(n!\) top and bottom and you are left with only \[(n+3)(n+2)(n+1)\]

Answer 9

it takes a bit of getting used to
we can do an example with numbers

Answer 10

if you don't distribute the 3 why is it n+3 and not n+1?

Answer 11

@satellite73

Answer 12

ok lets make sure it is clear what \((n+3)!\) means