SOLUTION: Simplify complex fraction 1+ 1/t-1 divided by 1- 1/t+1

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Question 363628: Simplify complex fraction
1+ 1/t-1 divided by 1- 1/t+1
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Since several similar problems were posted is a relatively short period of time, I am assuming that they all came from the same person. I already solved the first one (that I saw). And I will also do this one. For the other problems, I hope you can learn from these two solutions I have done.

%281%2B+1%2F%28t-1%29%29%2F%281-+1%2F%28t%2B1%29%29
This simplest way to simplify a complex fraction, IMHO, is to
  1. Find the Lowest Common Denominator (LCD) of all the denominators of the "little" fractions
  2. Multiply the numerator and denominator of the "big" fraction by the LCD found in step #1.

Let's see how this works on your complex fractions. The "little" fractions are 1%2F%28t-1%29 and 1%2F%28t%2B1%29. The LCD of t-1 and t+1 is simply their product: (t-1)(t+1). So we will multiply the numerator and denominator of the "big" fraction by (t-1)(t+1):

To multiply correctly we will need to use the Distributive Property in both the numerator and denominator:


%28t%5E2-1++%2B+%281%2F1%29%2A%28t%2B1%29%29%2F%28t%5E2-1+-+%281%2F1%29%2A%28t-1%29%29%29
%28t%5E2-1++%2B+t+%2B+1%29%2F%28t%5E2-1+-+%28t-1%29%29 (Be careful in the denominator! We need to subtract both the t and the -1, not just the t!)
Notice how all the "little" fractions disappear when you multiply by the LCD!
%28t%5E2+%2B+t%29%2F%28t%5E2+-+t%29
As usual, when your answer is a fraction, try to reduce it. The numerator and denominator can both be factored:
%28t%28t%2B1%29%29%2F%28t%28t-1%29%29
and the t's cancel:
%28cross%28t%29%28t%2B1%29%29%2F%28cross%28t%29%28t-1%29%29
leaving:
%28t%2B1%29%2F%28t-1%29