Question

simplify: 5/x^3 - 5/(x + h)^3/h.
I will attempt to write it using equation in the next post. the h is supposed to be under the whole of the rest of the equation.

Answer 1

\[5divx ^{3} - 5\div(x + h)^{3}divh\]

I'm not sure how to do it as an equation.

Answer 2

\[(5/x^3 - 5/(x+h)^3)/h\] ?

Answer 3

Yes

Answer 4

ok so the h is under everything

Answer 5

or is the h only under the last one

Answer 6

under the whole thing. Like with the brackets, that is how I should have done it.

Answer 7

ok

Answer 8

So keep the h out and do it last, and simplify the 2 other terms first by finding the least common denominator and then multiplying everything out and then simplifying again

Answer 9

Step 1: Predend the h isn't there and do it last. Step 2. Find the least common denominator for the two terms. Step 3: Combine terms. Step 4: Multiply out the numerator and re-factor as much as you can.

Answer 10

The least common denominator?

5/x^3 - 5/(x^3 + 2x^2h + 3xh^2 + h^3)

h^3?

Answer 11

or x^3 because there is one on both sides?

Answer 12

the least common denominator is (x^3)(x+h)^3. I'd keep it like that for now so it doesn't get too messy too soon.

Answer 13

lol this is already messy to me!

okay... 5(x + h)^3/(x^3)(x + h)^3 - 5(x)^3/(x + h)^3(x)^3

?

so then I can combine 5(x + h)^3 - 5x^3/x^3(x + h)^3

?

Answer 14

(5(x + h)^3 - 5x^3)/x^3(x + h)^3

Answer 15

Yes that is correct.

Answer 16

then I get, after cancelling 5x^3,

(15x^2h + 15xh^2 + 5h^3)/(x^3 + 3x^2h + 3xh^2 + h^3)(x^3)

and now I'm stuck again.

Answer 17

is x^3 * x^3 = x^6?

Answer 18

oh hang on, would it have been better to leave it intact?

Answer 19

no perhaps because then I would have to divide 5x^3 by the same.

Answer 20

Yeah I don't think you will need to expand the denominator; the only reason you would ever expand the denominator is if you thought you could expand and then factor the denominator differently such that you factor out a term from the numerator that could cancel with a term in the denominator.

Answer 21

So I'd leave it in tact for now

Answer 22

So, 5 - 5x^3/((x + h)^3)(x^3)

?

Answer 23

right now I've got the same as you've got: [15hx^2 + 15h^2x + 5h^3]/[(x^3)(x+h)^3] and that is after factoring and canceling that h from the beginning

Answer 24

I'm trying to see if that can be simplified further.

Answer 25

Woops that was before factoring out that h

Answer 26

So then it becomes: (15x^2 + 15xh + 5h^2) / [(x^3)(x+h)^3]

Answer 27

good :) I was wondering how you got that answer after the h factor

so you can remove a h from each part, both top and bottom?

Answer 28

oh, no, just the numerator at the very top?

Answer 29

Yeah only the numerator

Answer 30

Wow thanks so much for taking the time to help! This is so complicated, really appreciate it!

Answer 31

No problem. I think this is as simplified as it can get, as the roots of the numerator appear to be imaginary numbers.

Answer 32

Imaginary? lol okay :)

Answer 33

Oh I just read this: For polynomials in more than one variable the notion of root does not exist. So I guess it's as simplified as it can get.