SOLUTION: please help me...i'm getting sick with this problem..... {{{ 2+(1/(1-(1/x))) over 2-(3/(1-(1/x))) }}}

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Question 106011: please help me...i'm getting sick with this problem.....
+2%2B%281%2F%281-%281%2Fx%29%29%29+over+2-%283%2F%281-%281%2Fx%29%29%29+
Answer by chitra(359) About Me  (Show Source):
You can put this solution on YOUR website!
The given problem can be written as:

+2%2B%281%2F%281-%281%2Fx%29%29%29+over+2-%283%2F%281-%281%2Fx%29%29%29+

We first take the LCM of the terms that are present as the denominators in the entire expression. So that gives us.

+%28%282+%2B+%28x%2F%28x-1%29%29%29+%2F+%282+-+%283x%2F%28x+-+1%29%29%29+%29

Again taking LCM, we get:

%28%282%28x-1%29+%2B+x%29%2F%28x+-+1%29%29%2F%28%282%28x-1%29+-+3x%29%2F%28x-1%29%29

Here the (x - 1) term cancels out. So we get:

%28%282x+-+2+%2B+x%29%2F%282x+-+1+-+3x%29%29

==> %28x+-+2%29%2F%28-x+-+1%29

==> %28%282+-+x%29%2F%28x+%2B+1%29%29


thus the solution.