Divide the polynomial by the monomial denominator by writing the fraction as the sum (or difference) of fractions. Simplify your answer, if possible. 6x^4+3x^3−7/x^2

To divide the polynomial 6x^4 + 3x^3 - 7 by the monomial x^2, we can rewrite it as a fraction:

(6x^4 + 3x^3 - 7) / x^2

Now, let's simplify this expression by breaking it down into two separate terms:

6x^4 / x^2 + 3x^3 / x^2 - 7 / x^2

Simplify each term separately:

= 6x^(4-2) + 3x^(3-2) - 7x^(-2)
= 6x^2 + 3x - 7/x^2

So, the division of the polynomial by the monomial denominator is equal to:

6x^2 + 3x - 7/x^2