Answer:
1/2x^2 -5/6 +x^(-2)
Step-by-step explanation:
The sum can be separated into its components, and each of those simplified to the desired form.
Rewrite
[tex]\dfrac{3x^4-5x^2+6}{6x^2}=\dfrac{3x^4}{6x^2}+\dfrac{-5x^2}{6x^2}+\dfrac{6}{6x^2}\\\\=\boxed{\dfrac{1}{2}x^2-\dfrac{5}{6}+x^{-2}}[/tex]
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Additional comment
The rules of exponents tell you ...
(a^b)/(a^c) = a^(b-c)
