Complex Fraction: (27x^6 + 1)/(3x^3 + 18x^2 + x + 6)

[Tigertigre2000]

Simplify each expression:

. . .(27x^6 + 1) / (3x^3 + 18x^2 + x + 6)

My work:

. . .(27x^6 + 1) / [3x^2(x + 6) + 1(x + 6)]

. . .(27x^6 + 1) / [(3x^2 + 1)(x + 6)]

That's where I'm stuck. How would you factor out the first part.

I would really appriciate your reply, as soon as possible.

 

[Mrspi]

Re: Complex Fractions

Simplify each expression:

(27x^6+1)/ (3x^3+18x^2+x+6)

(27x^6+1)/ 3x^2(x+6)+1(x+6)
(27x^6+1)/ (3x^2+1)(x+6)

That's where I'm stuck. How would you factor out the first part.

I would really appriciate your reply, as soon as possible.

Did you notice that 27x^6 + 1 could be written as (3x^2)^3 + 1^3?

It's a difference of two cubes. Use this pattern to factor:
a^3 + b^3 = (a + b)(a^2 - ab + b^2)