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How do you simplify #(x^2+3x+2)/(x^2-1)#?

Answer 1

#(x+2)/(x+1)#

Factor the numerator and denominator.

For #x^2+3x+2,# consider two numbers which add up to equal #3# and multiply to equal #2.# The numbers #2,1# meet these criteria, so the factored form is

#(x+2)(x+1)#

For the denominator, recall the Difference of Squares, which tells us that

#x^2-a^2=(x+a)(x-a)#

Thus,

#x^2-1=(x+1)(x-1)#

We then have

#((x+2)cancel(x+1))/(cancel(x+1)(x-1))=(x+2)/(x+1)#

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Answer 2

Genesis Allen

To simplify the expression (x^2+3x+2)/(x^2-1), you can factor both the numerator and the denominator. The numerator can be factored as (x+1)(x+2), and the denominator can be factored as (x+1)(x-1).

Next, you can cancel out the common factor of (x+1) in both the numerator and the denominator.

After canceling out the common factor, the simplified expression becomes (x+2)/(x-1).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.