SOLUTION: <pre> Combine the rational expressions: x + 2 x - 4 8(x + 1) ————— + ————— + ———————— x - 7 7 - x x - 7 </pre>

x + 2     x - 4   8(x + 1)
—————  +  ————— + ————————
x - 7     7 - x    x - 7

We must get all the denominators the same.

Two of the denominators are already the same, 
but the 7 - x is not the same.  So let's work 
on it:

   7 - x

First write it in descending order:

  -x + 7

which is really

 -1x + 7

Now factor out -1 (which changes the sign of the 7)

 -1(x - 7)

and we can erase the 1

  -(x - 7)  

Now our original problem becomes:

x + 2      x - 4    8(x + 1)
—————  +  ——————  + ————————
x - 7    -(x - 7)    x - 7

Now take the - sign out in front of
that fraction making the + into a -

x + 2     x - 4   8(x + 1)
—————  -  ————— + ————————
x - 7     x - 7    x - 7

Now all the denominators are the same.

Distribute out the 8(x + 1) as 8x + 8

x + 2     x - 4    8x + 8
—————  -  ————— + ————————
x - 7     x - 7     x - 7

Put parentheses around the numerators:

(x + 2)     (x - 4)   (8x + 8)
———————  -  ——————— + ————————
 x - 7       x - 7      x - 7

Combine the numerators over the common 
denominator:

(x + 2) - (x - 4) + (8x + 8)
————————————————————————————
            x - 7

Remove the parentheses

 x + 2 - x + 4 + 8x + 8
————————————————————————
          x - 7

Combine like terms:

    8x + 14
   —————————
     x - 7

Edwin