SOLUTION: I need help finding the limits Problem: Find the limit of each using algebraic techniques. 1. lim x > -1 x^2 - 1/ x + 1 2. lim x > -1 2x^2 - x - 3/ x + 1 3. lim

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Question 1139284: I need help finding the limits
Problem:
Find the limit of each using algebraic techniques.
1. lim x > -1 x^2 - 1/ x + 1
2. lim x > -1 2x^2 - x - 3/ x + 1
3. lim x > 3 x - 3/ x^2 - 9

Image of the problems in case i typed them wrong: https://imgur.com/sIlPJJY

Answer by greenestamps(13215)   (Show Source): You can put this solution on YOUR website!


Factor numerator or denominator as appropriate in each example.

1. lim x > -1 (x^2 - 1)/ (x + 1)



The factored form shows that the rational function is equivalent to (x-1) everywhere that it is defined -- i.e., everywhere except when the denominator is zero, at x=-1. So the limit of the rational function as x approaches -1 is (-1-1) = -2.

The other two examples are very similar to that first one....

2. lim x > -1 (2x^2 - x - 3)/ (x + 1)

...

3. lim x > 3 (x - 3)/ (x^2 - 9)

...

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