## Limits: When not to Simplify?

Limits, differentiation, related rates, integration, trig integrals, etc.
Bruin
Posts: 2
Joined: Wed Apr 20, 2011 11:55 am
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### Limits: When not to Simplify?

Hello, simple limit question that has been on my mind. Is there a simple rule of thumb when not to simplify an equation?
Here is the problem that I have been working on:

lim as x ->2 of
(x^2+4x-12)/(x^2-2x)

If I simplify the above I get 1+(6/x), but (this is a big but) I totally miss the fact that in the original equation x != 2. Looking at it now, its fairly obvious that I did this wrong. My concern is that for a more complex problem the fact that x != some number might not be that apparent.

Is there any little tricks that I could use in other problems to know when not to simplify?

Thanks.

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
Contact:

### Re: Limits: When not to Simplify?

Hello, simple limit question that has been on my mind. Is there a simple rule of thumb when not to simplify an equation?
Here is the problem that I have been working on:

lim as x ->2 of
(x^2+4x-12)/(x^2-2x)

If I simplify the above I get 1+(6/x), but (this is a big but) I totally miss the fact that in the original equation x != 2. Looking at it now, its fairly obvious that I did this wrong. My concern is that for a more complex problem the fact that x != some number might not be that apparent.

Is there any little tricks that I could use in other problems to know when not to simplify?

Thanks.
$\frac{x^2+4x-12}{x^2-2x}=1+\frac{6}{x}$

Remember that when taking the limit as $x\to2$, $x$ never takes the value of 2. Therefore it doesn't matter that the LHS is not defined at 2 and the RHS is.

Bruin
Posts: 2
Joined: Wed Apr 20, 2011 11:55 am
Contact:

### Re: Limits: When not to Simplify?

Thanks Martingale for the reply. I think I understand whats going on here a little better.