Question 1041309
{{{(27a^3-8b^3)/(b^2-b-6)}}}{{{"×"}}}{{{(bc-b-3c^""+3)/(3ac^""-2bc-3a+2b)}}}

Factor all the numerators and denominators:

{{{27a^3-8b^3}}}{{{""=""}}}{{{(3a)^3-(2b)^3}}}{{{""=""}}}{{{(3a-2b)((3a)^2+(3a)(2b)+(2b)^2)}}}{{{""=""}}}{{{(3a-2b)(9a^2+6ab+4b^2)}}}

{{{b^2-b-6}}}{{{""=""}}}{{{(b-3)(b+2)}}}

{{{bc-b-3c+3}}}{{{""=""}}}{{{b(c-1)-3(c-1)}}}{{{""=""}}}{{{(b-3)(c-1)}}}

{{{3ac-2bc-3a+2b}}}{{{""=""}}}{{{c(3a-2b)-(3a-2b)}}}{{{""=""}}}{{{(c-1)(3a-2b)}}}

 
{{{((3a^""-2b)(9a^2+6ab+4b^2))/((b^""-3)(b^""+2))}}}{{{"×"}}}{{{((b^""-3)(c^""-1))/((c^""-1)(3a^""-2b))}}}

Cancel the (3a-2b)'s

{{{((cross(3a^""-2b))(9a^2+6ab+4b^2))/((b^""-3)(b^""+2))}}}{{{"×"}}}{{{((b^""-3)(c^""-1))/((c^""-1)(cross(3a^""-2b)))}}}

Cancel the (b-3)'s

{{{((cross(3a^""-2b))(9a^2+6ab+4b^2))/((cross(b^""-3))(b^""+2))}}}{{{"×"}}}{{{((cross(b^""-3))(c^""-1))/((c^""-1)(cross(3a^""-2b)))}}}

Cancel the (c-1)'s

{{{((cross(3a^""-2b))(9a^2+6ab+4b^2))/((cross(b^""-3))(b^""+2))}}}{{{"×"}}}{{{((cross(b^""-3))(cross(c^""-1)))/((cross(c^""-1))(cross(3a^""-2b)))}}}

All that left is:

{{{(9a^2+6ab+4b^2)/(b^""+2)}}}