Question

(x^-1+4x^-2)/(1-16x^-2)

Answer 1

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

multiply top and bottom by x^2
= ( 1/x + 4/x^2) / (1 - 16/x^2) * (x^2/x^2)
Since I am multiplying by 1, I am not changing the value of my fraction , simply its appearance

= (x+4)/(x^2 - 16)
= (x+4)/( (x+4)(x-4) )
= 1/(x-4) , x ≠ -4 (or else we divided by zero)