(x+3)/(x^2-2x-8)-(x-5)/(x^2-12x+32) Perform the indicated operation(s) and simplify

To be able to perform the indicated operation(s) on (x+3)/(x^2-2x-8)-(x-5)/(x^2-12x+32) , we have to express them as similar fractions.
Apply factoring on each expression on the denominator side.
Let:
 x^2-2x-8=(x+2)(x-4)
and
 x^2-12x+32=(x-4)(x-8)
Determine the LCD by getting the product of the distinct factors from denominator side of each term.
Thus, LCD =(x+2)(x-4)(x-8)
                  =(x^2-2x-8)(x-8)
                  = x^3-2x^2-8x-8x^2+16x+64
                   =x^3-10x^2+8x+64
Express each term by the LCD. Multiply top and bottom of each term by the missing factor.
First term:
(x+3)/(x^2-2x-8) =(x+3)/((x+2)(x-4))
                =(x+3)/((x+2)(x-4))*(x-8)/(x-8)
                =((x-8)(x+3))/((x+2)(x-4)(x-8))   
                =(x^2-5x-24)/(x^3-10x^2+8x+64)
Second term:
(x-5)/(x^2-12x+32) =(x-5)/((x-4)(x-8))
                  =(x-5)/((x-4)(x-8)) *(x+2)/(x+2)
                  =((x-5)(x+2))/((x-4)(x-8)(x+2))
                   =(x^2-5x+2x-10)/(x^3-10x^2+8x+64)
                  =(x^2-3x-10)/(x^3-10x^2+8x+64)
Applying the equivalent fraction in terms of LCD, we get:
(x+3)/(x^2-2x-8)-(x-5)/(x^2-12x+32)
=(x^2-5x-24)/(x^3-10x^2+8x+64) -(x^2-3x-10)/(x^3-10x^2+8x+64)
=((x^2-5x-24) -(x^2-3x-10))/(x^3-10x^2+8x+64)
=(x^2-5x-24 -x^2+3x+10)/(x^3-10x^2+8x+64)
=(x^2-x^2-5x+3x-24+10)/(x^3-10x^2+8x+64)
=(0-2x-14)/(x^3-10x^2+8x+64) 
=(-2x-14)/(x^3-10x^2+8x+64) or -(2x+14)/(x^3-10x^2+8x+64)
Final answer:
(x+3)/(x^2-2x-8)-(x-5)/(x^2-12x+32)=-(2x+14)/(x^3-10x^2+8x+64)