(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

lim_{x→3}(x^{2}+5x+2) ÷ x^{2}-6x+9

2. The attempt at a solution

You cannot solve through direct substitution because the denominator comes out to equal 0, and you cannot divide by 0. Thus, I factored the lower terms to reach the following:

(x-3)^{2}or (x-3)(x-3).

However, to my knowledge I cannot do this to the numerator, as ±1 & ±2 do not add up to 5 in any way, shape, or form. As such, I manipulated (x^{2}+5x+2) into the following:

x(x+5)+2

But I am not sure where to go from here as the denominator still adds up to 0, and I am not sure of how to simplify any further. As of right now I have:

x(x+5)+2 ÷ (x-3)(x-3)

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# Homework Help: Using Algebraic Manipulation to evaluate a limit

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