# Reaching my limits

1. Feb 5, 2013

### MSchott

1. The problem statement, all variables and given/known data
lim x->4 (1/((sqrt x)-2))-4/(x-4)

2. Relevant equations

3. 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.

2. Feb 5, 2013

### micromass

Staff Emeritus
Add up the two fractions.

3. Feb 5, 2013

### MSchott

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

4. Feb 5, 2013

### micromass

Staff Emeritus
5. Feb 5, 2013

### Staff: Mentor

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.

6. Feb 8, 2013

### 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:
$(x-4)(sqrt (x) -2)/(Sqrt (x)+2)(x-2)$

7. Feb 8, 2013

### Staff: Mentor

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.

Last edited: Feb 8, 2013