## anonymous one year ago Solve

1. anonymous

$\lim x->4 =(\sqrt{x+5}-3)/x-4$

2. anonymous

Any help.

3. misty1212

HI!!

4. misty1212

you do get $$\frac{0}{0}$$ when you plug in right?

5. misty1212

gimmick here is to multiply numerator and denominator by the conjugate of the numerator to rationalize it do you know what i am talking about?

6. theopenstudyowl

Rationalize the numerator....

7. anonymous

$\frac{\sqrt{x+5}-3}{x-4}\times \frac{\sqrt{x+5}+3}{\sqrt{x+5}+3}$ ois what @misty1212 is telling you to do

8. anonymous

leave the denominator in factored form just multiply up top

9. misty1212

yeah that you good from there?

10. anonymous

Oh, thanks!

11. anonymous

I would always FOIL the denominator too, which was my issue.

12. misty1212

$\color\magenta\heartsuit$

13. anonymous

oh no don't do that you should expect the $$x-4$$ to cancel, do don't multiply out

14. anonymous

Yeah, I saw it just now, that makes sense, thanks again! I got 1/6 just to confirm.

15. misty1212

that looks good

16. anonymous

Alright thanks again guys!

17. misty1212

lol guess i cam a guy now

18. anonymous

yw

19. anonymous

yeah you look like a guy!

20. anonymous

Oh, I was referring to both of you haha