Help Solving Limits: x-4sqrt(x)+4/(x-4)(sqrt(x)-2)

[alexpratt]

i know how to solve limits, but i have trouble seeing if i can factor anymore or if the limit just doesn't exist, which is the case with the next few questions

Homework Statement

1/(sqrt(x)-2) - 4/(x-4)

Homework Equations

The Attempt at a Solution

this is what i have now, i don't think i can do anything else, but I am probably wrong.
And i have written that the limit doesn't exist.

x-4sqrt(x)+4/(x-4)(sqrt(x)-2)and sorry if the equation is written the wrong way or anything, with the square roots and everything!

 

[╔(σ_σ)╝]

I am assuming the limit is as x approaches 4.

The limit does in fact exist.

You should try rationalizing , that is,

\frac{1}{ \sqrt{x} -2} \frac{ \sqrt{x}+2}{ \sqrt{x}+2}

 

[alexpratt]

yes, it is as x approaches 4, sorry about that.

but when i rationalize it, wouldn't i just get x-4 in the denominator which would still be division by zero?
i'll see if i can figure it out considering you said the limit exists, thank you

 

[╔(σ_σ)╝]

Rationalize and then add what you get to - 4/(x-4).

They have the same denominator now, right ?

Then, see if you can factor anything out from the "new" function.

 

[alexpratt]

-1/4?and just so i know in the future, how did you get the square root sign?

 

[eumyang]

-1/4?

I didn't get that answer; you're close, though.

 

[╔(σ_σ)╝]

-1/4?

The answer should be 1/4 .

I am sure you just made a little sign error.

and just so i know in the future, how did you get the square root sign?

The symbols are written from Latex

https://www.physicsforums.com/misc/howtolatex.pdf

 

[alexpratt]

I keep getting -1/4

I know you guys are right though, i graphed it to make sure, not that i thought you were wrong haha.
I have no clue where I am going wrong though.

thanks for your help though

 

[╔(σ_σ)╝]

Show me your steps so I can point out the error.

 

[alexpratt]

i figured it out, i was rationalizing the left side but i forgot to get a common denominator afterwards.