How do you simplify (x^2-x-6)/(4x^3)*(x+1)/(x^2+5x+5)x2−x−64x3⋅x+1x2+5x+5?

1 Answer
George C.
Jul 18, 2015

Try factoring and find:

(x^2-x-6)/(4x^3)*(x+1)/(x^2+5x+5)x2−x−64x3⋅x+1x2+5x+5

=((x-3)(x+2)(x+1))/(4x^3(x+(5+sqrt(5))/2)(x+(5-sqrt(5))/2))=(x−3)(x+2)(x+1)4x3(x+5+√52)(x+5−√52) (factoring)

=(x^3-7x-6)/(4x^5+20x^4+20x^3)=x3−7x−64x5+20x4+20x3 (multiplying)

Explanation:

Going in one direction, multiply up to get:

(x^2-x-6)/(4x^3)*(x+1)/(x^2+5x+5)x2−x−64x3⋅x+1x2+5x+5

=((x^2-x-6)(x+1))/(4x^3(x^2+5x+5))=(x2−x−6)(x+1)4x3(x2+5x+5)

=(x^3-7x-6)/(4x^5+20x^4+20x^3)=x3−7x−64x5+20x4+20x3

Going in the other direction, factor to get:

(x^2-x-6)/(4x^3)*(x+1)/(x^2+5x+5)x2−x−64x3⋅x+1x2+5x+5

((x-3)(x+2))/(4x^3)*(x+1)/(x^2+5x+5)(x−3)(x+2)4x3⋅x+1x2+5x+5

=((x-3)(x+2)(x+1))/(4x^3(x+(5+sqrt(5))/2)(x+(5-sqrt(5))/2))=(x−3)(x+2)(x+1)4x3(x+5+√52)(x+5−√52)

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

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