Question 131889
{{{((4d^2)/(5d^2-30d+45))((5d-15)/(2d))}}} Start with the given expression


{{{((2*2*d*d)/(5d^2-30d+45))((5d-15)/(2d))}}}   Factor {{{4d^2}}} to get {{{2*2*d*d}}} 


{{{((2*2*d*d)/(5(d-3)(d-3)))((5d-15)/(2d))}}}   Factor {{{5d^2-30d+45}}} to get {{{5(d-3)(d-3)}}} 


{{{((2*2*d*d)/(5(d-3)(d-3)))((5(d-3))/(2d))}}}   Factor {{{5d-15}}} to get {{{5(d-3)}}} 


{{{((2*2*d*d)/(5(d-3)(d-3)))((5(d-3))/(2(d)))}}}   Factor {{{2d}}} to get {{{2(d)}}} 



{{{(2*2*d*d)5(d-3)/(5(d-3)(d-3)2(d))}}} Combine the fractions



{{{(cross(2)*2*d*cross(d))cross(5)cross((d-3))/(cross(5)cross((d-3))(d-3)cross(2)cross(d))}}} Cancel like terms



{{{(2d)/(d-3)}}} Simplify




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Answer:



So {{{((4d^2)/(5d^2-30d+45))((5d-15)/(2d))}}} simplifies to {{{(2d)/(d-3)}}} 


In other words,  {{{((4d^2)/(5d^2-30d+45))((5d-15)/(2d))=(2d)/(d-3)}}}