Hi, I´m having trouble solving this limit, without using the L´Hospital.

$\displaystyle limit_{x\to\infty}(\frac{2x+3}{2x+1})^x$

I tried dividing it into a sum and using Newtons binomial, but i arrived at

$\displaystyle limit_{x\to\infty}(\frac{4,481}{1+(1/2x)})^x$

which i am not able to solve. The answer should be e.