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

1 Answer
Apr 8, 2018

Answer:

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

Explanation:

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)#