0=(x^2-4x-32)/(x^2-16)

Solution for 0=(x^2-4x-32)/(x^2-16) equation:

D( x )

x^2-16 = 0

x^2-16 = 0

x^2-16 = 0

1*x^2 = 16 // : 1

x^2 = 16

x^2 = 16 // ^ 1/2

abs(x) = 4

x = 4 or x = -4

x in (-oo:-4) U (-4:4) U (4:+oo)

0 = (x^2-(4*x)-32)/(x^2-16) // - (x^2-(4*x)-32)/(x^2-16)

0-((x^2-(4*x)-32)/(x^2-16)) = 0

-((x^2-4*x-32)/(x^2-16)) = 0

(-1*(x^2-4*x-32))/(x^2-16) = 0

x^2-4*x-32 = 0

x^2-4*x-32 = 0

DELTA = (-4)^2-(-32*1*4)

DELTA = 144

DELTA > 0

x = (144^(1/2)+4)/(1*2) or x = (4-144^(1/2))/(1*2)

x = 8 or x = -4

(x+4)*(x-8) = 0

(-1*(x+4)*(x-8))/(x^2-16) = 0

( -1 )

-1 = 0

x belongs to the empty set

( x+4 )

x+4 = 0 // - 4

x = -4

( x-8 )

x-8 = 0 // + 8

x = 8

x in { -4} 

x = 8