Question 132474
{{{((4x^2-13x+3)/(8x^2-2x))((6x^2+6x)/(x^2-6x+9))}}} Start with the given expression


{{{(((x-3)(4x-1))/(8x^2-2x))((6x^2+6x)/(x^2-6x+9))}}}   Factor {{{4x^2-13x+3}}} to get {{{(x-3)(4x-1)}}} 


{{{(((x-3)(4x-1))/(2x(4x-1)))((6x^2+6x)/(x^2-6x+9))}}}   Factor {{{8x^2-2x}}} to get {{{2x(4x-1)}}} 


{{{(((x-3)(4x-1))/(2x(4x-1)))((6x(x+1))/(x^2-6x+9))}}}   Factor {{{6x^2+6x}}} to get {{{6x(x+1)}}} 


{{{(((x-3)(4x-1))/(2x(4x-1)))((6x(x+1))/((x-3)(x-3)))}}}   Factor {{{x^2-6x+9}}} to get {{{(x-3)(x-3)}}} 



{{{(x-3)(4x-1)6x(x+1)/2x(4x-1)(x-3)(x-3)}}} Combine the fractions



{{{cross((x-3))cross((4x-1))6cross(x)(x+1)/(2cross(x)*cross((4x-1))cross((x-3))(x-3))}}} Cancel like terms


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


{{{3(x+1)/(x-3)}}} Reduce {{{6/2}}} to get {{{3/1}}}




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Answer:


So {{{((4x^2-13x+3)/(8x^2-2x))((6x^2+6x)/(x^2-6x+9))}}} simplifies to {{{3(x+1)/(x-3)}}} 



{{{((4x^2-13x+3)/(8x^2-2x))((6x^2+6x)/(x^2-6x+9))=3(x+1)/(x-3)}}}