1. ## Another Limits Question

I have the following question on a worksheet:

$
lim ((2/x+2)-(3/x-1))/(x+8)
$

With $x$ approaching $8$.

I simplified the equation to:

$
lim ((2x-2)-(3x+6))/((x-1)(x+2))/(x+8)
$

I Know that I should factor out the denominator in the upper portion, but I am unsure as to how I would do so.

2. Originally Posted by Jd09
I have the following question on a worksheet:

$
lim ((2/x+2)-(3/x-1))/(x+8)
$

With $x$ approaching $8$.

I simplified the equation to:

$
lim ((2x-2)-(3x+6))/((x-1)(x+2))/(x+8)
$

I Know that I should factor out the denominator in the upper portion, but I am unsure as to how I would do so.
$\displaystyle \frac{\frac{2}{x+2} - \frac{3}{x-1}}{x+8} = \frac{2(x-1)-3(x+2)}{(x+8)(x+2)(x-1)} = \frac{-x -8}{(x+8)(x+2)(x-1)}$

3. Actually for this one you don't need to simplify it first. You can plug x = 8 in directly. Always try this first and see if there is a Mathematical problem in doing so. Then you know if you have to try to simplify it.

-Dan

4. Originally Posted by topsquark
Actually for this one you don't need to simplify it first. You can plug x = 8 in directly. Always try this first and see if there is a Mathematical problem in doing so. Then you know if you have to try to simplify it.

-Dan
I suspect the OP has made a typo and it's x --> -8 rather than 8.