Question 3328
Here's your cartoon:
{{{
cartoon( 
  ((X^2+3x-10)/(6X^2-24)) / ((X^2+X-20)/(X^2+3X+2)) / ((x^2-1)/6),
  ((X^2+3x-10)/(6X^2-24)) / ((X^2+X-20)/highlight((X^2+3X+2))) / ((x^2-1)/highlight(6)),
  6*(x^2+3x-10)*(x^2+3x+2)/(6x^2-24)/(x^2+x-20)/(x^2-1),
  6*highlight((x^2+3x-10))*(x^2+3x+2)/(6x^2-24)/(x^2+x-20)/(x^2-1),
  6*highlight((x-2)(x+5))*(x^2+3x+2)/(6x^2-24)/(x^2+x-20)/(x^2-1),
  6*(x-2)(x+5)*highlight((x^2+3x+2))/(6x^2-24)/(x^2+x-20)/(x^2-1),
  6*(x-2)(x+5)*highlight((x+1)*(x+2))/(6x^2-24)/(x^2+x-20)/(x^2-1),
  6*(x-2)(x+5)*(x+1)(x+2)/highlight((6x^2-24))/(x^2+x-20)/(x^2-1),
  6*(x-2)(x+5)*(x+1)(x+2) / highlight(6*(x-2)*(x+2))/(x^2+x-20)/(x^2-1),
  6*(x-2)(x+5)*(x+1)(x+2) / 6/(x-2)/(x+2)/highlight((x^2+x-20))/(x^2-1),
  6*(x-2)(x+5)*(x+1)(x+2) / 6/(x-2)/(x+2)/highlight((x-4)*(x+5))/(x^2-1),
  6*(x-2)(x+5)*(x+1)(x+2) / 6/(x-2)/(x+2)/(x-4)/(x+5)/highlight((x^2-1)),
  6*(x-2)(x+5)*(x+1)(x+2) / 6/(x-2)/(x+2)/(x-4)/(x+5)/highlight((x-1)*(x+1)),
  6*(x-2)(x+5)*(x+1)(x+2) / 6/(x-2)/(x+2)/(x-4)/(x+5)/(x-1)/(x+1),
  highlight(6)*highlight((x-2))*highlight((x+5))*highlight((x+1))*highlight((x+2)) / highlight(6)/highlight((x-2))/highlight((x+2))/(x-4)/highlight((x+5))/(x-1)/highlight((x+1)),
  cross(6)*cross((x-2))*cross((x+5))*cross((x+1))*cross((x+2)) / cross(6)/cross((x-2))/cross((x+2))/(x-4)/cross((x+5))/(x-1)/cross((x+1)),
  highlight(1/(x-4)/(x-1))
)
}}}

And here's your full solution.

First, move things around:

{{{ ((X^2+3x-10)/(6X^2-24))/((X^2+X-20)/(X^2+3X+2))/((x^2-1)/6)=6*(x^2+3x-10)*(x^2+3x+2)/(6x^2-24)/(x^2+x-20)/(x^2-1)}}}

Second, factorize every piece in that formula using <A HREF=/algebra/homework/quadratic/>Quadratic Equation Solver</A>.

{{{ 1x^2+3x-10 = (x-2)(x+5)}}}
{{{ 6X^2-24 =  6(x-2)(x+2) }}}
{{{ X^2+X-20 =  (x-4)(x+5) }}}
{{{ X^2+3X+2 =  (x+1)(x+2) }}}
{{{ x^2-1 = (x-1)*(x+1)    }}}

{{{ ((X^2+3x-10)/(6X^2-24))/((X^2+X-20)/(X^2+3X+2))/((x^2-1)/6)
=
6*(x^2+3x-10)*(x^2+3x+2)/(6x^2-24)/(x^2+x-20)/(x^2-1)
=
6*(x-2)(x+5)*(x+1)(x+2) / 6/(x-2)/(x+2)/(x-4)/(x+5)/(x-1)/(x+1)
}}}

Now, similar terms cancel out:

{{{
6*(x-2)(x+5)*(x+1)(x+2) / 6/(x-2)/(x+2)/(x-4)/(x+5)/(x-1)/(x+1)
=
cross(6)*cross((x-2))*cross((x+5))*cross((x+1))*cross((x+2)) / cross(6)/cross((x-2))/cross((x+2))/(x-4)/cross((x+5))/(x-1)/cross((x+1))
= 1/(x-4)/(x-1)}}}

So, your answer is 

{{{((X^2+3x-10)/(6X^2-24)) / ((X^2+X-20)/(X^2+3X+2)) / ((x^2-1)/6) = 1/(x-4)/(x-1)}}}.

Double check my solution, maybe I got something wrong.

Also, note that for every thing that canceled out, there is a point where the