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

1 Answer
Jul 18, 2015

Answer:

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)

Explanation:

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.