Question 158059
{{{((x^3+96-6x^2-16x)/(3x^3-648))/((4x^2+16x-64)/(6x^2-26x+216))}}} Start with the given expression.



{{{((x^3+96-6x^2-16x)/(3x^3-648))((6x^2-26x+216)/(4x^2+16x-64))}}} Multiply the first fraction {{{(x^3+96-6x^2-16x)/(3x^3-648)}}} by the reciprocal of the second fraction {{{(4x^2+16x-64)/(6x^2-26x+216)}}}.



{{{(((x-4)*(x-6)*(x+4))/(3x^3-648))((6x^2-26x+216)/(4x^2+16x-64))}}} Factor {{{x^3+96-6x^2-16x}}} to get {{{(x-4)*(x-6)*(x+4)}}} (hint graph the expression).



{{{(((x-4)*(x-6)*(x+4))/(3*(x-6)*(x^2+6*x+36)))((6x^2-26x+216)/(4x^2+16x-64))}}} Factor {{{3x^3-648}}} to get {{{3*(x-6)*(x^2+6*x+36)}}} (hint use the difference of cubes).




{{{((x-4)*(x-6)*(x+4)(6*x^2-26*x+216))/(3*(x-6)*(x^2+6*x+36)(4*x^2+16*x-64))}}} Combine the fractions. 



{{{((x-4)highlight((x-6))(x+4)(6*x^2-26*x+216))/(3*highlight((x-6))(x^2+6*x+36)(4*x^2+16*x-64))}}} Highlight the common terms. 



{{{((x-4)cross((x-6))(x+4)(6*x^2-26*x+216))/((3)cross((x-6))(x^2+6*x+36)(4*x^2+16*x-64))}}} Cancel out the common terms. 



{{{((x-4)(x+4)(6*x^2-26*x+216))/(3(x^2+6*x+36)(4*x^2+16*x-64))}}} Simplify. 





So {{{((x^3+96-6x^2-16x)/(3x^3-648))/((4x^2+16x-64)/(6x^2-26x+216))}}} simplifies to {{{((x-4)(x+4)(6*x^2-26*x+216))/(3(x^2+6*x+36)(4*x^2+16*x-64))}}}.




Note: the answer is not as "simple" as I think it should be. Double check the problem to make sure that you copied it correctly