Question 144593
{{{((2*2*c*c)/(3c^2-12c+12))((3c-6)/(2c))}}} Start with the given expression



{{{((2*2*c*c)/(3c^2-12c+12))((3c-6)/(2c))}}} Factor {{{4c^2}}} to get {{{2*2*c*c}}}



{{{((2*2*c*c)/(3(c-2)(c-2)))((3c-6)/(2c))}}}   Factor {{{3c^2-12c+12}}} to get {{{3(c-2)(c-2)}}} 



{{{((2*2*c*c)/(3(c-2)(c-2)))((3(c-2))/(2c))}}}   Factor {{{3c-6}}} to get {{{3(c-2)}}} 



{{{(2*2*c*c*3(c-2))/(3(c-2)(c-2)(2c))}}} Combine the fractions



{{{(cross(2)*2*cross(c)*c*cross(3)cross((c-2)))/(cross(3)cross((c-2))(c-2)(cross(2)cross(c)))}}} Cancel like terms




{{{(2c)/(c-2)}}} Simplify




So {{{((4c^2)/(3c^2-12c+12))((3c-6)/(2c))}}} simplifies to {{{(2c)/(c-2)}}}. In other words, {{{((4c^2)/(3c^2-12c+12))((3c-6)/(2c))=(2c)/(c-2)}}} where {{{c<>0}}} and {{{c<>2}}}