Another Limits Question

**Jd09** · February 8th 2011, 05:17 PM

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.

**mr fantastic** · February 8th 2011, 05:51 PM

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.

$\displaystyle \frac{\frac{2}{x+2} - \frac{3}{x-1}}{x+8} = \frac{2(x-1)-3(x+2)}{(x+8)(x+2)(x-1)} = \frac{-x -8}{(x+8)(x+2)(x-1)}$

**topsquark** · February 8th 2011, 06:01 PM

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

**mr fantastic** · February 8th 2011, 07:43 PM

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.

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