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

`( x^(3) )/( x^(2) -4): ( x^(3) -9 x^(2) )/( x^(2) +7x-18)= \\ = ( x^(3) )/((x+2)(x-2))* ( x^(2) +7x-18)/( x^(2) (x-9))= \\ = ( x^(3) )/((x+2)(x-2))* ((x-2)(x+9))/( x^(2) (x-9))= \\ = (x(x+9))/((x+2)(x-9))`