How do you simplify #(x^2-x-6)/(4x^3)*(x+1)/(x^2+5x+5)#?

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Answer 1 · 2015-07-18T12:24:54

Try factoring and find:

#(x^2-x-6)/(4x^3)*(x+1)/(x^2+5x+5)#

#=((x-3)(x+2)(x+1))/(4x^3(x+(5+sqrt(5))/2)(x+(5-sqrt(5))/2))# (factoring)

#=(x^3-7x-6)/(4x^5+20x^4+20x^3)# (multiplying)

Going in one direction, multiply up to get:

#(x^2-x-6)/(4x^3)*(x+1)/(x^2+5x+5)#

#=((x^2-x-6)(x+1))/(4x^3(x^2+5x+5))#

#=(x^3-7x-6)/(4x^5+20x^4+20x^3)#

Going in the other direction, factor to get:

#(x^2-x-6)/(4x^3)*(x+1)/(x^2+5x+5)#

#((x-3)(x+2))/(4x^3)*(x+1)/(x^2+5x+5)#

#=((x-3)(x+2)(x+1))/(4x^3(x+(5+sqrt(5))/2)(x+(5-sqrt(5))/2))#

No common factors to cancel, so this cannot be simplified.