SOLUTION: Solve for x:{{{(4x+3)/(x-6)+(x-4)/(6-x)=44/(2x-12)}}}

All the denominators are in descending order except
the denominator 6-x.  So we first get it in descending
order -x+6.  Since it begins with a negative sign we
factor out the negative and that changes the signs
inside the parentheses:
        6-x = -x+6 = -(x-6)

Then we factor the denominator 2x-12 as 2(x-6)

 

We bring the negative sign of denominator -(x-6) in 
front of the fraction.  

Also on the right of the equal sign we can cancel
the 2 into the 44 and get 22:

  

Now the LCD is just x-6.  So we multiply through
by that and get:











Edwin