SOLUTION: I NEED HELP {{{(3/(x-5)+1)/(1-4/(x-5))}}} I need to simplify Thank you

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Question 89233: I NEED HELP
%283%2F%28x-5%29%2B1%29%2F%281-4%2F%28x-5%29%29
I need to simplify
Thank you
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!

%283%2F%28x-5%29%2B1%29%2F%281-4%2F%28x-5%29%29

Write the 1's as 1%2F1 so everything
will be fractions:

%283%2F%28x-5%29%2B1%2F1%29%2F%281%2F1-4%2F%28x-5%29%29

Put parentheses around the top and bottom:

%28%283%2F%28x-5%29%2B1%2F1%29%29%2F%28%281%2F1-4%2F%28x-5%29%29%29

The LCD of all four denominators is +x-5+.
Put it over 1 and put parentheses around it, +%28%28x-5%29%2F1%29
Then multiply top and bottom by that:

 

Now use the distributive principle to remove the 
parentheses on the right:



Cancel the x-5%29's in the top left and the bottom right
terms and erase the 1's and we get

%283+%2B+%28x-5%29%29%2F%28%28x-5%29-4%29

Remove the parentheses and we get:

%283%2Bx-5%29%2F%28x-5-4%29

Combining terms on top and bottom, we end up with

%28x-2%29%2F%28x-9%29

Edwin