solve

[jolly thistle]

my answer is 5 but according to a website the answer is 8, so anyone can help me

[knotty osprey]

I can see your image

So, the thing you usually do with limits of that form

Let me write it down

$\lim_{x\to a} \dfrac{f(x)}{\sqrt{g(x)} - \sqrt{h(x)}}$

[queen cradle]

Poncelet

[knotty osprey]

You multiply and divide by the conjugate of what you have in the denominator

Basically that will be in this case

$\lim_{x\to a} \dfrac{f(x)}{\sqrt{g(x)} - \sqrt{h(x)}}\cdot \dfrac{\sqrt{g(x)}+\sqrt{h(x)}}{\sqrt{g(x)}+\sqrt{h(x)}}$

[queen cradle]

Poncelet

[knotty osprey]

And then you multiply

And the square roots will wipe out in the denominator

So in this example

maybe let him try the rest?

or at least what you suggested?

I see that you are well-versed and passionate, @knotty osprey but we are here to guide, aren't we?

[jolly thistle]

I have tried my answer is 5 but there is a website on google it says that the answer is 8

[knotty osprey]

$\lim_{x\to 2} \dfrac{x^2-4}{\sqrt{3x-2}-\sqrt{x+2}} = \lim_{x\to 2} \dfrac{x^2-4}{\sqrt{3x-2}-\sqrt{x+2}}\dfrac{\sqrt{3x-2}+\sqrt{x+2}}{\sqrt{3x-2}+\sqrt{x+2}} = \lim_{x\to 2} \dfrac{(x^2-4)(\sqrt{3x-2}+\sqrt{x+2})}{3x-2-x-2}$

[queen cradle]

Poncelet

[knotty osprey]

Well, that's better

btw, this is usually the first thing you should try in limits of this type

[knotty osprey]

show us your work

[jolly thistle]

wait

[knotty osprey]

we will help you find the error together

[knotty osprey]

This could fail, which in this case will lead you to a 0/0 indetermination or something like that. In that case, you can try using l'Hôpital's rule if it's legal

[knotty osprey]

I see

You got a typo

You should multiply x+2 by everything there, not just by the first square root

you forgot paratheses

line 3 from the bottom

Yep

[jolly thistle]

Damn
Got it lemme try it

[knotty osprey]

Well done on everything else ✨

Yeah, everything else is fine

[jolly thistle]

yo Thanks a lot I got the answer