Question

Rewrite the following as three reduced terms using fractional coefficients and negative exponents if needed:
3x^4-5x^2+6
———————
6x^2

Answer 1

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

  $\dfrac{3x^4-5x^2+6}{6x^2}=\dfrac{3x^4}{6x^2}+\dfrac{-5x^2}{6x^2}+\dfrac{6}{6x^2}\\\\=\boxed{\dfrac{1}{2}x^2-\dfrac{5}{6}+x^{-2}}$

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Additional comment

The rules of exponents tell you ...

  (a^b)/(a^c) = a^(b-c)