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

Question

2080 views around the world

You can reuse this answer
Creative Commons License

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.

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