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How do you simplify #(x^2+5x+6)/(x+1) * (x^2-1)/(x+3)#?

Answer 1

Eva Abramson

#x^2 + x - 3#

#(x^2 + 5x + 6)/ (x+1)# • #(x^2 - 1)/ (x+3) #

Factor out the numerators:

# ((x+3)(x+2))/(x+1)# • #((x+1)(x-1))/(x+3)#

Cross simplify to get:

#(x+2)/1# • #(x-1)/1#

Make it into factoring:

#(x+2)# • #(x-1)#

You get:

#x^2 + x - 3#

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Answer 2

Isaiah Anthony

To simplify the expression (x^2+5x+6)/(x+1) * (x^2-1)/(x+3), we can first factor the numerator and denominator of each fraction.

The numerator of the first fraction, x^2+5x+6, can be factored as (x+2)(x+3). The denominator of the first fraction, x+1, cannot be factored further.

The numerator of the second fraction, x^2-1, can be factored as (x+1)(x-1). The denominator of the second fraction, x+3, cannot be factored further.

Now, we can cancel out common factors between the numerators and denominators.

(x^2+5x+6)/(x+1) * (x^2-1)/(x+3) simplifies to [(x+2)(x+3)/(x+1)] * [(x+1)(x-1)/(x+3)].

Next, we can cancel out the common factors (x+1) and (x+3) in the numerator and denominator.

The simplified expression is (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.