SOLUTION: 12.) Complete complex fraction. I really need help on this one! 2/x+1/x-2 1/x-2- 3/x

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Question 164254This question is from textbook Elementary and Intermediate
: 12.) Complete complex fraction. I really need help on this one!
2/x+1/x-2
1/x-2- 3/x


This question is from textbook Elementary and Intermediate

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282%2Fx%2B1%2F%28x-2%29%29%2F%281%2F%28x-2%29-3%2Fx%29 Start with the given expression


Multiply EVERY term by the LCD x%28x-2%29 to clear out the inner denominators


%282%28x-2%29%2Bx%29%2F%28x-3%28x-2%29%29 Multiply and simplify


%282x-4%2Bx%29%2F%28x-3x%2B6%29 Distribute


%283x-4%29%2F%28-2x%2B6%29 Combine like terms.


%283x-4%29%2F%28-%282x-6%29%29 Factor a negative one from the denominator


-%283x-4%29%2F%282x-6%29 Simplify


So %282%2Fx%2B1%2F%28x-2%29%29%2F%281%2F%28x-2%29-3%2Fx%29 simplifies to -%283x-4%29%2F%282x-6%29