Verified answer

x^4-3x^3/x^2-9 = x^3(x-3)/{x^2-(3)^2}

=x^3(x-3)/(x+3)(x-3) = x^3/(x+3)

Question is incorrect and SHOULD be shown as :-

(x^4 - 3x^3) / (x^2 - 9)

x^3 (x - 3)

----------------

(x - 3)(x + 3)

x^3

-----------

x + 3