Hello everybody. I just need a little help with some very basic Calculus. Actually I need help with the Algebra part, but it is a Calculus problem. Here is the problem.
Lim x->-2 of (x^2+3x+2)/(2-|x|)

That is it and I know the answer is -1, but I cannot get that |x| out of the denomenator, I have tried to multiply by the conjugate, but that did not seem to work. Thanks in andave for any advice.

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Is it x^2+3x+2 or x^2+3x-2?

He must mean
$$\lim_{x\rightarrow -2}\frac{x^2+3x+2}{2-|x|}$$
Otherwise it's undefined.

I edited my post and Vegeta was correct.

AKG
Homework Helper
As x approaches -2, x is negative.

Think of the absolute value funciton as a piecewise function, defined separately for positive numbers and negative numbers.

Yes and keep in my to factor x^2+3x+2

I have thought of it as a piecewise function, but my instructions are to solve this algebraically. I have also factored it ((x+1)(x+2))/(2-|x|). Now what? Thanks for the help.

Defining piecewise functions is an algebraic method.

As you approach -2 from left and right, lxl is defined as -x. Try to use this.

x is having the negative value in this case then IxI will have I-2I=-2
so the 2-IXI term will be 4 simple

HallsofIvy