SOLUTION: Add and simplify: 1/x-1 - 4/x^2-1 + 2/x+1 Find the product: (3x-7)(2x+4)

Algebra ->  Equations -> SOLUTION: Add and simplify: 1/x-1 - 4/x^2-1 + 2/x+1 Find the product: (3x-7)(2x+4)       Log On


   

Question 148470: Add and simplify:
1/x-1 - 4/x^2-1 + 2/x+1
Find the product:
(3x-7)(2x+4)

Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!
1. %281%2F%28x-1%29%29+-+%284%2F%28x%5E2-1%29%29+%2B+%282%2F%28x%2B1%29%29

Factor x%5E2-1
%281%2F%28x-1%29%29+-+%284%2F%28x-1%29%28x%2B1%29%29+%2B+%282%2F%28x%2B1%29%29

Multiply %281%2F%28x-1%29%29 by %28x%2B1%29%2F%28x%2B1%29
and %282%2F%28x%2B1%29%29 by %28x-1%29%2F%28x-1%29



Simplify the numerators



Add the numerators over a single denominator

%28%28%28x%2B1%29-%284%29%2B%282x-2%29%29%2F%28x-1%29%28x%2B1%29%29

Combine like terms in the numerator

%28%283x-5%29%2F%28x-1%29%28x%2B1%29%29
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2.Find the product:
(3x-7)(2x+4)
F.O.I.L.
First Outside Inside Last

First (terms):
(3x)(2x) or 6x%5E2

+

Outside (terms):
(3x)(4) or 12x

+

Inside (terms):
(-7)(2x) or -14x

+

Last (terms):
(-7)(4) or -28

Add the results:
6x%5E2%2B12x%2B-14x-28

Combine like terms (the x terms)

6x%5E2-2x-28