You must learn to factor in order to do this kind of problem.



You must learn to factor the lower left denominator by grouping:

x³+3x²-9x-27
x²(x+3)-9(x+3)
(x+3)(x²-9)
(x+3)(x-3)(x+3)

You must learn to factor the upper right numerator either by the
AC method or by the guess and check method:

6x²+19x+3
(6x+1)(x+3)

You must learn to factor the lower right denominator by taking out
a common factor:

18x²+3x
3x(6x+1)




Indicate the multiplication of numerators and denominators
making just one fraction:
        


Now you can cancel what will cancel.  You can do it all in one step,
but I'll just cancel one thing at a time:

Cancel the 3 on the bottom into the 18 on top, getting 6 on top:





Cancel the x on the bottom into the x4 on top, getting x3
on top:

    ³




Cancel the (6x+1)'s:







Cancel the (x+3)'s





You can leave it like that, since nothing else will cancel.
As I said above you can do all that canceling in one step.

Edwin