Math Help - L'Hospitals Rule ---- easy quick help

1. L'Hospitals Rule ---- easy quick help

Find lim as n--> infinity of 2n/(1+3sqrt(n))

since its infinity over infinity use L'Hospitals rule

2 / (3/2 n^-1/2)

2(3/2 sqrt(n))

OK so i know this is wrong and i know it should be

2sqrt(n) / (3/2)

but i dont get why only the n^(-1/2) comes up to the top and the 3/2 stays in the denominator cause i thought the 3/2 and n^-1/2 should go up top since they are connected (multiplying).

2. Originally Posted by mybrohshi5
Find lim as n--> infinity of 2n/(1+3sqrt(n))

since its infinity over infinity use L'Hospitals rule

2 / (3/2 n^-1/2)

2(3/2 sqrt(n))

OK so i know this is wrong and i know it should be

2sqrt(n) / (3/2)

but i dont get why only the n^(-1/2) comes up to the top and the 3/2 stays in the denominator cause i thought the 3/2 and n^-1/2 should go up top since they are connected (multiplying).
2/(3/2)*n^-1/2
= 2*(n^1/2)/(3/2)

3. I understand that it is 2*(n^1/2)/(3/2) but i dont get why it is this. why doesnt the (3/2) go to the numerator along with the n^-1/2 since they are "attatched to one another"

4. Originally Posted by mybrohshi5
I understand that it is 2*(n^1/2)/(3/2) but i dont get why it is this. why doesnt the (3/2) go to the numerator along with the n^-1/2 since they are "attatched to one another"
When 3/2 goes to numerator it becomes (3/2)^-1 = 2/3