Question

Question #d4dce

Answer 1

See below.

Explanation:

First, get rid of the fraction by multiplying everything by `x`

`2x^2 + 36000/x => 2x^3 +36000`

Now we take out the `HCF` of each term, in this case `2`

`2x^3+36000 => 2(x^3 + 18000)`

Answer 2

`(2(x^3+18000))/x`

Explanation:

Let's set `y` to equal `2x^2+36000/x`

We have:

`y=2x^2+36000/x` Multiply both sides by `x`.

`xy=x(2x^2+36000/x)`Distribute

`xy=2x^3+36000`

`xy=2*x*x*x+2*2*2*2*2*3*3*5*5*5`

We ask ourselves: What do `2*x*x*x` and `2*2*2*2*2*3*3*5*5*5` share in common?

We see that they share a `2`

We factor. (Take out a two from each term)

`xy=2(x*x*x+2*2*2*2*3*3*5*5*5)`

`xy=2(x^3+18000)`

We now divide both sides by `x`.

`y=(2(x^3+18000))/x`

This is equal to what we started with (`2x^2+36000/x`) because they both equal `y`.

The answer is `(2(x^3+18000))/x`