Question 1041844
<pre>
{{{(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)

{{{(4x+3)/(x-6)+(x-4)/(-(x-6))=44/(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:

{{{(4x+3)/(x-6)-(x-4)/(x-6)=22/(x-6)}}}  

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

{{{(4x+3)-(x-4)=22}}}

{{{4x+3-x+4=22}}}

{{{3x+7=22}}}

{{{3x=15}}}

{{{x=5}}}

Edwin</pre>