SOLUTION: I need help simplifying complex rational expression I tried method 2 w/lcd x-4/x-1 - x/x-3 ___________ _____ 3+ 12/x-3

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Question 278468: I need help simplifying complex rational expression I tried method 2 w/lcd
x-4/x-1 - x/x-3
_________________
3+ 12/x-3
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x-4%29%2F%28x-1%29+-+x%2F%28x-3%29%29%2F%283%2B+12%2F%28x-3%29%29
The LCD of all the "little" fractions is the right approach. The LCD here is:
(x-1)(x-3)
Multiplying the numerator and denominator of the "big" fraction by the LCD we get:

To multiply this we need to use the Distributive Property on both the numerator and denominator:

Now we can start canceling:

leaving:
%28%28x-3%29%28x-4%29+-+%28x-1%29%28x%29%29%2F%28%28x-1%29%28x-3%293%2B+%28x-1%29%2812%29%29
Now we can finally multiply:

Combining like terms we get:
%28-6x+%2B+12%29%2F%283x%5E2+-+3%29
Now we can reduce the fraction. To reduce fractions you cancel factors which are common to the numerator and denominator. So we need factors:
%28-6%28x+-2%29%29%2F%283%28x%5E2+-+1%29%29
%28-6%28x+-2%29%29%2F%283%28x%2B1%29%28x+-+1%29%29
A factor of 3 will cancel:
%28-2%28x+-2%29%29%2F%28%28x%2B1%29%28x+-+1%29%29
No more reducing is possible so we'll multiply out the top and bottom:
%28-2x%2B4%29%2F%28x%5E2+-1%29