Question 144816
 {{{((x^2-9)/(x-2))((x^2-4)/(x-3))}}}


Both of the numerators are the difference of two squares, so factor them:


{{{((x+3)(x-3)/(x-2))((x+2)(x-2)/(x-3))}}}


Multiply numerators and denominators, just like you would any other fractions:


{{{((x+3)(x-3)(x+2)(x-2))/((x-2)(x-3))}}}


Eliminate factors common to both numerator and denominator because {{{a/a=1}}} for all real {{{a}}}:


{{{((x+3)*cross((x-3))(x+2)*cross((x-2)))/(cross((x-2))*cross((x-3)))=(x+3)(x+2)=green(x^2+5x+6)}}}


And that's really how it works, really.  Commit that "difference of two squares" factorization pattern to memory, you will see it and need to use it many times before you have completed all of your math education.