Verified Answer :

syed514

x^3/x^2-4/x^3-9x^2/x^2+7x-18
factor everything so you know what to cancel out;

Also, take the bottom "fraction"; turn it over, spank it, and multiply it to the top "fraction"; like this:
      xxx                          (x+9)(x-2)
           --------- * ----------

          (x-2)(x+2) xx (x-9)

Now cancel like terms top to bottom

    x(x+9)

    ----------

  (x+2) (x-9)

HomertheGenius

\(\frac{ x^{3} }{ x^{2} -4}: \frac{ x^{3} -9 x^{2} }{ x^{2} +7x-18}= \\ = \frac{ x^{3} }{(x+2)(x-2)}* \frac{ x^{2} +7x-18}{ x^{2} (x-9)}= \\ = \frac{ x^{3} }{(x+2)(x-2)}* \frac{(x-2)(x+9)}{ x^{2} (x-9)}= \\ = \frac{x(x+9)}{(x+2)(x-9)}\)

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