what is (x+3)!/(x+4)! simplified?

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what is (x+3)!/(x+4)! simplified?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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hmm, If I'm not mistaken, I think it's the same as the following:\[(k+1)! = k!(k+1)\] so, as for your question : \[\frac{x!(x+3)}{x!(x+4)} = \frac{x+3}{x+4}\] not sure though ^_^
You draw a pyramid from 1,2,3....(x-1), (x-2), (x-3),...(x)...(x+1), (x+2), (x+3), (x+4). Build a pyramid like the Egyptians did.
._. I never used that way lol

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(x+3)!/(x+4)! = (x+3)!/ /( x+4)(x+3)!= 1/(x+4)
(k+1)!=k!(k+1) is only true for that case. All you are doing is expanding the factorial, it's not a factorial property or anything
thank you all!
I think I got my pyramid wrong, the x-1's should go the other way ...(x-3), (x-2), (x-1)...

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