Simplify:( x/x^2-16 -1/x-4)/4/x+4 The Quotient of Two Rational Expressions

Simplify:( x/x^2-16
-1/x-4)/4/x+4.

Solution:

{x/(x^2-16)
- 1/(x-4)}/ (4/(x+4)) or

{[x/(x^2-16-1)/(x-4)]/4 }/x and
then add .

Such cases arise as there is no unique
representation by using sufficient brackets.

I take the 1st
choice of freedom of putting bracket.

 (a/b)/(c/d) =
ad/bc.

x/(x^2-16) - 1/(x-4) = [x- (x+4)]/(x^2-16), as x^-16
is made the common
denominator.

=4/(x^2-16).

So
{x/x^2-16)-1/(x-4)}/{4/(x+4)] = -4
(x+4)/[(x^2-16)4

{x/x^2-16)-1/(x-4)}/{4/(x+4)]=
-(x+4)/(x^2-16) 

{x/x^2-16)-1/(x-4)}/{4/(x+4)]=
-(x+4)/(x-4)(x+4)

{x/x^2-16)-1/(x-4)}/{4/(x+4)] =
1/(x-4)