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

1/2x^2 -5/6 +x^(-2)

Explanation:

The sum can be separated into its components, and each of those simplified to the desired form.

Rewrite

`(3x^4-5x^2+6)/(6x^2)=(3x^4)/(6x^2)+(-5x^2)/(6x^2)+(6)/(6x^2)\\\\=\boxed{(1)/(2)x^2-(5)/(6)+x^(-2)}`

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Additional comment

The rules of exponents tell you ...

(a^b)/(a^c) = a^(b-c)