SOLUTION: How did x+2 be the answer to ((x)+(2x/(x-2))) divided by ((1)+ (4/(x^2-4))) ? and How did 3/8 be the answer to 3^(n+2) + (3^(n+3) - 3^(n+1)) ? Sorry I'm still confused.

Algebra ->  Equations -> SOLUTION: How did x+2 be the answer to ((x)+(2x/(x-2))) divided by ((1)+ (4/(x^2-4))) ? and How did 3/8 be the answer to 3^(n+2) + (3^(n+3) - 3^(n+1)) ? Sorry I'm still confused.      Log On


   

Question 998501: How did x+2 be the answer to ((x)+(2x/(x-2))) divided by ((1)+ (4/(x^2-4))) ?
and
How did 3/8 be the answer to 3^(n+2) + (3^(n+3) - 3^(n+1)) ?

Sorry I'm still confused. Thank you!
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Here is the first one, done through ordinary fraction skills, although with the given variable and variable expressions. No kind of long division was needed.

Your two starting rational expressions are the dividend and the divisor. Arrange each of these
into a separate single rational expression.
x%2B%282x%29%2F%28x-2%29 DIVIDED BY 1%2B4%2F%28x%5E2-4%29

Meaning of that quotient as COMPLEX FRACTION is %28x%2B%282x%29%2F%28x-2%29%29%2F%281%2B4%2F%28x%5E2-4%29%29.
Examine carefully and find that the simplest common denominator is x%5E2-4=%28x-2%29%28x%2B2%29. Multiply
the entire complex fraction by 1=%28%28x-2%29%28x%2B2%29%29%2F%28%28x-2%29%28x%2B2%29%29.




I may be condensing some steps but you may need to do some work to see that any sub-steps will agree.

%28x%28x-2%29%28x%2B2%29%2B2x%28x%2B2%29%29%2F%28%28x-2%29%28x%2B2%29%2B4%29

%28%28x%28x-2%29%2B2x%29%28x%2B2%29%29%2F%28x%5E2-4%2B4%29

%28%28x%5E2-2x%2B2x%29%28x%2B2%29%29%2F%28x%5E2-4%2B4%29

%28x%5E2%28x%2B2%29%29%2F%28x%5E2%29

%28cross%28x%5E2%29%28x%2B2%29%29%2F%28cross%28x%5E2%29%29

highlight%28x%2B2%29