# Thread: Help solving a limit

1. ## Help solving a limit

Hello, im trying to solve the following limit:

I've tried to multiply the entire expression by:

So I could take the square root out of the numerator, but i don't know what to do next, i tried to factor the numerator to x(x+3) and cancel with the (x+3) which appears in the denominator but i don't know what to do next.
I'm not allowed to use L'Hopital rule
I need some help...

Sorry for my english.

2. ## Re: Help solving a limit

Originally Posted by LucasSG
Hello, im trying to solve the following limit:

$\frac{{\sqrt {{x^2} + 16} - 5}}{{{x^2} + 3x}} = \frac{{{x^2} - 9}}{{x\left( {x + 3} \right)\left( {\sqrt {{x^2} + 16} + 5} \right)}} = \frac{{x - 3}}{{x\left( {\sqrt {{x^2} + 16} + 5} \right)}}$.