SOLUTION: Add and Simplify: 1/x-2 - 4/x^2-4 + 3/x+2

Algebra ->  Equations -> SOLUTION: Add and Simplify: 1/x-2 - 4/x^2-4 + 3/x+2      Log On


   

Question 149635: Add and Simplify:
1/x-2 - 4/x^2-4 + 3/x+2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F%28x-2%29+-+4%2F%28x%5E2-4%29+%2B+3%2F%28x%2B2%29 Start with the given expression.


1%2F%28x-2%29+-+4%2F%28%28x-2%29%28x%2B2%29%29+%2B+3%2F%28x%2B2%29 Factor x%5E2-4 to get %28x-2%29%28x%2B2%29


So the LCD is %28x-2%29%28x%2B2%29


Multiply the first fraction by %28x%2B2%29%2F%28x%2B2%29. Multiply the third fraction by %28x-2%29%2F%28x-2%29. Doing this will make each denominator the LCD %28x-2%29%28x%2B2%29



Combine the fractions.


Distribute


%28x%2B2-4%2B3x-6%29%2F%28%28x-2%29%28x%2B2%29%29 Since the denominators are equal, we can combine the numerators of the common denominator.


%284x-8%29%2F%28%28x-2%29%28x%2B2%29%29 Combine like terms.


%284%28x-2%29%29%2F%28%28x-2%29%28x%2B2%29%29 Factor out the GCF 4 from the numerator.


%284highlight%28%28x-2%29%29%29%2F%28highlight%28%28x-2%29%29%28x%2B2%29%29 Highlight the common terms.


%284cross%28%28x-2%29%29%29%2F%28cross%28%28x-2%29%29%28x%2B2%29%29 Cancel out the common terms.


%284%29%2F%28x%2B2%29 Simplify.


So 1%2F%28x-2%29+-+4%2F%28x%5E2-4%29+%2B+3%2F%28x%2B2%29 simplifies to %284%29%2F%28x%2B2%29


In other words, 1%2F%28x-2%29-4%2F%28x%5E2-4%29%2B3%2F%28x%2B2%29=%284%29%2F%28x%2B2%29 where x%3C%3E-2 or x%3C%3E2