Question

x^2-4/sqrt(x^2+5)-3

Answer 1

multiply by the conjugate

Answer 2

How? Can you show me plz?

Answer 3

conjugate is like multiply by the opposite.. as in the difference of two perfect squares:
(a+b)(a-b)

Answer 4

http://www.wolframalpha.com/input/?i=%28x%5E2-4%29%2F%28sqrt%28x%5E2%2B5%29-3%29

tada :)

Answer 5

oh ok thanks a lot!!!

Answer 6

\[\frac{x^{2} -4}{\sqrt{x^{2}+5}-3}*\frac{\sqrt{x^{2}+5}+3}{\sqrt{x^{2}+5}+3} = \frac{(x^{2}-4)(\sqrt{x^{2}+5}+3)}{(x^{2}-4)}\]

Answer 7

umm I'm confusing!

Answer 8

you are confused?
\[(\sqrt{x^{2}+5}-3) *(\sqrt{x^{2}+5}+3) = (\sqrt{x^{2}+5})^{2} - 9 = x^{2} +5-9 = x^{2} -4\]
does that help?

Answer 9

Is this the final answer? I mean this is the limit for this function, isn't?

Answer 10

you didnt ask to find a limit...all you posted was an expression
we assumed you need to simplify it by rationalizing the denominator

if there are instructions, you need to provide this in the original post or we cant help you !!??

Answer 11

I'm looking for determining the limit for (x^2-4)/(sqrt(x^2+5)-3) when x approaches -2?

Answer 12

well after looking at the simplified expressions , did you try plugging in x=-2

Answer 13

I somehow knew this was a limit problem just by looking at it

Answer 14

I plugged x=-2 I got 0/0 it is indeterminate!

Answer 15

i know thats why we multiplied by the conjugate to get into different form
plug -2 into simplified expression

Answer 16

L'hopital's rule?

Answer 17

why would you use l'hopitals rule after we just went through all the work of rationalizing the denominator?

i mean l'hopitals will work of course...but they may not have learned derivatives yet...

Answer 18

@dumbcow right, sorry about that

Answer 19

unfortunately you are taught limits first , then derivatives, so a shortcut like l'hopitals only is useful after the fact
such is the irony of math at times :)

Answer 20

where did shahadanware go?
if you plug in x=-2, you get the limit to be 6
\[\frac{x^{2}-4}{\sqrt{x^{2}+5}-3} \rightarrow \sqrt{x^{2}+5} +3 \]
you can verify this
http://www.wolframalpha.com/input/?i=lim+x-%3E-2+%28x%5E2-4%29%2F%28sqrt%28x%5E2%2B5%29-3%29