Question 78330
{{{((2x^2-2)/(6x+6))*((6x^2+18x)/(x^2+2x-3))}}}


{{{((2x^2-2)/(6(x+1)))*((6x^2+18x)/(x^2+2x-3))}}} Factor a 6 out of {{{6x+6}}}


{{{(2(x^2-1)/(6(x+1)))*((6x^2+18x)/(x^2+2x-3))}}} Factor a 2 out of {{{2x^2-2}}}


{{{(2(x^2-1)/(6(x+1)))*(6x(x+3)/(x^2+2x-3))}}} Factor a 6x out of {{{6x^2+18x}}}


Now factor {{{x^2-1}}}


*[invoke factoring_quadratics 1, 0, -1]


Now factor {{{x^2+2x-3}}}

*[invoke factoring_quadratics 1, 2, -3]


So after all of that we get 

{{{(2((x-1)(x+1))/(6(x+1)))*(6x(x+3)/((x-1)(x+3)))}}}


{{{(2(cross((x-1))cross((x+1)))/(6cross((x+1))))*(6x*cross((x+3))/(cross((x-1))cross((x+3))))}}} Notice these terms cancel

So we're left with

{{{(2/6)*(6x/1)}}}


{{{(2*6x/6)}}} Multiply


{{{(12x/6)}}}


{{{2x}}} Divide 

So the expression {{{((2x^2-2)/(6x+6))*((6x^2+18x)/(x^2+2x-3))}}} reduces to 

{{{2x}}}