SOLUTION: I can't seem to figure out this problem, can someone please help me? 1-2/x ----- x-4/x

Algebra ->  Equations -> SOLUTION: I can't seem to figure out this problem, can someone please help me? 1-2/x ----- x-4/x      Log On


   

Question 145491: I can't seem to figure out this problem, can someone please help me?
1-2/x
-----
x-4/x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%281-2%2Fx%29%2F%28x-4%2Fx%29 Start with the given expression


%28x%281-2%2Fx%29%29%2F%28x%28x-4%2Fx%29%29 Multiply both the numerator and the denominator by the LCD x


Distribute. Notice how the inner denominators cancel


%28x-2%29%2F%28x%5E2-4%29 Simplify

%28x-2%29%2F%28%28x-2%29%2A%28x%2B2%29%29 Factor x%5E2-4 to get %28x-2%29%2A%28x%2B2%29.


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


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


1%2F%28%28x%2B2%29%29 Simplify.


So %281-2%2Fx%29%2F%28x-4%2Fx%29 simplifies to 1%2F%28%28x%2B2%29%29.


In other words, %281-2%2Fx%29%2F%28x-4%2Fx%29=1%2F%28%28x%2B2%29%29 where x%3C%3E0, x%3C%3E-2, or x%3C%3E2