limit with square root

[letsgetaway]

I circled the steps I don't understand. In the numerator it is x-3 then changes to sqrt(x-3). I tried to multiply by the conjugate of the denominator but I'm not getting the same solution.

 

[galactus]

That's just a property of radicals.

\(\displaystyle \frac{a}{\sqrt{a}}=\sqrt{a}\)

In your case:

\(\displaystyle \L\\\frac{x-3}{\sqrt{x-3}}=\sqrt{x-3}\)

 

[letsgetaway]

thanks for clearing that up for me, g! i appreciate your help.