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I'd need you guys to check it in a minute.

\[\implies{(2x^{3 \over 2} - 4x^{-1 \over 2}) - 8x^{3 \over 2} \over (x^2 - 2)^2} \]

\[\implies {{-6x^{3 \over 2}} - {4x^{1 \over 2} }\over(x^2 - 2)^2} \]

Can I simplify it more?

you can factorise the numerator i suppose

Oh, yes. Is there anything else?

Using wolfram, I'm not getting the same answer as that

Oh... I might be wrong in that case.

Can we integrate that and check?

i cant see any problem with your answer

So then am I correct?

Your exponent on the 4 was positive when it was supposed to be negative.

Oh, I mistakenly made that positive when it was negative in the previous step.
*close enough*

oh yes - just a typo

You can then factor the \[\frac{1}{\sqrt{x}}\]out, and make it look significantly simpler.

Thank you again!

well done parth - just a human error

Thank you @cwrw238. Your encouragement much appreciated.

OK sir. Thank you for your help.