Question 133259
{{{((6x-18)/(2x^2-5x+3))((4x^2+4x+1)/(6x+3))}}} Start with the given expression


{{{(((2*3)(x-3))/(2x^2-5x+3))((4x^2+4x+1)/(6x+3))}}}   Factor {{{6x-18}}} to get {{{6(x-3)}}} and factor 6 to get {{{(2*3)}}} 


{{{(((2*3)(x-3))/((2x-3)(x-1)))((4x^2+4x+1)/(6x+3))}}}   Factor {{{2x^2-5x+3}}} to get {{{(2x-3)(x-1)}}} 


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


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



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



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



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




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Answer:


So {{{((6x-18)/(2x^2-5x+3))((4x^2+4x+1)/(6x+3))}}} simplifies to {{{(2(x-3)(2x+1))/((2x-3)(x-1))}}}. In other words {{{((6x-18)/(2x^2-5x+3))((4x^2+4x+1)/(6x+3))=(2(x-3)(2x+1))/((2x-3)(x-1))}}}