Solving lim x->4 (1/((sqrt x)-2))-4/(x-4)

[MSchott]

Homework Statement

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

Homework Equations

The Attempt at a Solution

I have made several stabs at this problem. First I tried using values very close to 4 (e.g. sqrt of 4.001) Then I tried rationalizing the expression 1/((sqrt x) -2). That did not work. I also tried the LCD b. Nothing gets me closer to the answer which is 1/4. Pleae help.

 

[micromass]

Add up the two fractions.

 

[MSchott]

like so: x-4sqrtx+4/(sqrtx-2)(x-4) Then what?

 

[micromass]

Try to factorize the numerator.

PS I would appreciate it very much if you would try to make your posts in LaTeX. It is much easier for us. Here is a tutorial: https://www.physicsforums.com/showpost.php?p=3977517&postcount=3

 

[Mark44]

PS I would appreciate it very much if you would try to make your posts in LaTeX. It is much easier for us.

like so: x-4sqrtx+4/(sqrtx-2)(x-4) Then what?

I would appreciate it, as well. Here's what you wrote:

$$ x - 4\sqrt{x} + \frac{4}{\sqrt{x} - 2} (x - 4)$$

This is probably not what you meant, though.

 

[MSchott]

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

Here is the LaTex version of the problem Thanks for your help leading me to LaTex. I am still unable to solve the problem. When I combine the fractions using a common denominator I get:
(x-4)(sqrt (x) -2)/(Sqrt (x)+2)(x-2)

 

[Mark44]

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

Here is the LaTex version of the problem Thanks for your help leading me to LaTex. I am still unable to solve the problem. When I combine the fractions using a common denominator I get:
(x-4)(sqrt (x) -2)/(Sqrt (x)+2)(x-2)

I don't see how you got that.
Starting from here:
$$ \frac{1}{\sqrt{x} - 2} - \frac{4}{x - 4}$$

the denominator will be (√x - 2)(x - 4), and not (√x + 2)(x - 2) as you show.

It wouldn't hurt to review some basic algebra, especially how to add fractions.