Simplify x-2/x^3-8?

Answer 1

x-2 / (x-2)(x^2 + 2x + 4) = 1/ x^2 + 2x + 4

Answer 2

Simplify x-2/x^3-8=(x-2)/(x-2(x^2+2x+4)=1/[x^2+2x+4)

Answer 3

I just want to help the answer above..

he factored out (x-2) because in the denominator,
x^3-8, if you plug in 2, it is going to be zero.
In a function, if it can be zero by pluging in a certain number,
it means you can factor it out with x= the number..

since you can make zero with x= 2, you can factor it out
as (x-2). Then, you can do (x^3-8)/(x-2) :) and the x-2 cancels out.

Answer 4

the quickest way of doing this is to try to factor out x-2 from x^3-8
using long division. first make sure the original equation has all the different x factors

so x^3-8 becomes (x^3+0x^2+0x-8)

1x^2+2x+4
--------------------
x-2 |(x^3+0x^2+0x-8)
x^3-2x^2
----------
2x^2+0x-8
2x^2-4x
------------
4x-8
4x-8
------
0

So (x^3-8)=(x-2)*(1x^2+2x+4)

so your original equation becomes

(x-2)
---------------------- =
(x-2)*(1x^2+2x+4)
1
-----------------
x^2+2x+4

Answer 5

The denominator can be factored to give a (x-2) term and a quadratic. Then you wind up with
1/(quadratic).