limit as x is approaching -4 (sqrt(x^2+9)-5)/(x^2-3x-4)

Thanks in advance!

Question

limit as x is approaching -4    (sqrt(x^2+9)-5)/(x^2-3x-4)

Thanks in advance!

hartnn · Answer

could you factorize denominator ?

hartnn · Answer

for numerator, you need to rationalize it
by multiplying and dividing by  (sqrt(x^2+9)+5)

anonymous · Answer

By sqrt(x^2+9)-5?

hartnn · Answer

to rationalize, we multiply and divide by the conjugate!
so its 
 (sqrt(x^2+9)+5)

anonymous · Answer

Oh right! I hope I rememberr that..

hartnn · Answer

you will :)
so, do that and tell me what u get ?

anonymous · Answer

Okay! So I'm at (x-4)/(sqrt(x^2+9+5))

anonymous · Answer

Unless I've done something wrong, now what?

hartnn · Answer

/(x^2-3x-4) = ... ?
what factors did u get ?

anonymous · Answer

Well after I rationalized, I saw I could cancel out the top and bottom (x+4)

hartnn · Answer

wait, is the question correct ? the denominator ? 
because the denominator would be (x-4)(x+1) right ? so there will be no x+4 there/......

hartnn · Answer

if the denominator is /(x^2-3x-4) 
then you can directly plug in x=-4
no need to do anything else

anonymous · Answer

FFFFFF I was doing the wrong problem! I'm sorry! The denominator is /(x^2-3x-4) for sure

hartnn · Answer

if the denominator is /(x^2-3x-4) 
then you can directly plug in x=-4
no need to do anything else

hartnn · Answer

so what u get if you directly put x=-4 ?

hartnn · Answer

there ?