Question

Simplify the expression:

Answer 1

what is the expression?

Answer 2

Getting there...it's a long one.

Answer 3

\[-\frac{2x ^{2}}{ 3\sqrt[3]{x ^{2}-1}^{4} }+\frac{ 1 }{ \sqrt[3]{x ^{2}-1}}\]

Answer 4

So it's legible \[\Large -\frac{2x ^{2}}{ 3\sqrt[3]{x ^{2}-1}^{4} }+\frac{ 1 }{ \sqrt[3]{x ^{2}-1}} \]
You can probably rationalize the denominators (get rid of the radicals) right at the start and use that to add them

Answer 5

It might help to see how to rationalize them if you rewrite the exponents like so\[\Large -\frac{2x ^{2}}{ 3(x ^{2}-1)^{4/3} }+\frac{ 1 }{ (x ^{2}-1)^{1/3}} \]

Answer 6

So if I multiply the second term by \[\frac{ 3(x ^{2}-1) }{ 3(x ^{2}-1) }\] I'll end up with a common denominator and 3(x^2+1) in the top?

I'm really bad at exponents!!

Answer 7

Yes!! I know that's it. I have the answer. I just could NOT see how to get there. Thank you for adjusting my perspective. :)

Answer 8

But do you need to get rid of the radicals in the denominator? or just get them as one fraction?

Answer 9

No, I just need to get them as one fraction. It's a second derivative and I'm checking for concavity and points of inflection. :)

Answer 10

Ah so you prob have it equal to zero, so who cares if the denominator isn't mathematically "correct" :D

Answer 11

Or "improper" :D

Answer 12

Exactly. I just could not get an idea how to combine those. I just needed a friendly reminder kick in the right direction. I really appreciate your help!