Question 76470
The given expression is: 


{{{ (16-x^2)/(x^3 - 2x^2 - 8x)}}} 


The expression in the numerator is in the form of {{{a^2 - b^2}}} 


The expansion of this is:  (a + b)(a - b) 


The numerator can be written as:  (4 + x)(4 - x)


And in the denominator: we can take x as the common factor and hence the denominator can be written as:   {{{x(x^2 - 2x - 8)}}} 


This can be factored as:  {{{x(x + 2)(x - 4)}}} 


Hence, the expression can be written as: 


{{{((4 + x)(4 - x))/x(x + 2)(x - 4)}}} 


Taking the negative sign in the numerator, we get: 


{{{-(4 + x)(x - 4)/x(x + 2)(x - 4)}}}  



{{{ (-4 - x)(cross(x - 4))/x(x + 2)(cross(x - 4))}}} 


Thus, the final expression is: 


{{{(-x - 4)/x(x + 2)}}} 


OR 


{{{ (-(x + 4))/x(x + 2)}}}


Hence, the solution.