Question

SOLVE. x cubed over x squared - 4 divided by x cubed - 9x squared over x squared + 7x -18

Answer 1

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)

Answer 2

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