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OpenStudy (anonymous):

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.

OpenStudy (anonymous):

\[5divx ^{3} - 5\div(x + h)^{3}divh\] I'm not sure how to do it as an equation.

OpenStudy (anonymous):

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

OpenStudy (anonymous):

Yes

OpenStudy (anonymous):

ok so the h is under everything

OpenStudy (anonymous):

or is the h only under the last one

OpenStudy (anonymous):

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

OpenStudy (anonymous):

ok

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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.

OpenStudy (anonymous):

The least common denominator? 5/x^3 - 5/(x^3 + 2x^2h + 3xh^2 + h^3) h^3?

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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.

OpenStudy (anonymous):

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 ?

OpenStudy (anonymous):

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

OpenStudy (anonymous):

Yes that is correct.

OpenStudy (anonymous):

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.

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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.

OpenStudy (anonymous):

So I'd leave it in tact for now

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

Woops that was before factoring out that h

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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?

OpenStudy (anonymous):

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

OpenStudy (anonymous):

Yeah only the numerator

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

Imaginary? lol okay :)

OpenStudy (anonymous):

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.

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