Answer :
To simplify
$$
\frac{4x^7 + 6x^6 + 9x^3}{-x^2},
$$
we can divide each term in the numerator by the denominator.
1. Divide the first term:
$$
\frac{4x^7}{-x^2} = -4x^{7-2} = -4x^5.
$$
2. Divide the second term:
$$
\frac{6x^6}{-x^2} = -6x^{6-2} = -6x^4.
$$
3. Divide the third term:
$$
\frac{9x^3}{-x^2} = -9x^{3-2} = -9x.
$$
Now, combining all these results gives:
$$
-4x^5 - 6x^4 - 9x.
$$
This expression can also be factored by taking $x$ as a common factor:
$$
-4x^5 - 6x^4 - 9x = x(-4x^4 - 6x^3 - 9).
$$
Thus, the simplified answer is
$$
-4x^5 - 6x^4 - 9x \quad \text{or equivalently} \quad x(-4x^4 - 6x^3 - 9).
$$
$$
\frac{4x^7 + 6x^6 + 9x^3}{-x^2},
$$
we can divide each term in the numerator by the denominator.
1. Divide the first term:
$$
\frac{4x^7}{-x^2} = -4x^{7-2} = -4x^5.
$$
2. Divide the second term:
$$
\frac{6x^6}{-x^2} = -6x^{6-2} = -6x^4.
$$
3. Divide the third term:
$$
\frac{9x^3}{-x^2} = -9x^{3-2} = -9x.
$$
Now, combining all these results gives:
$$
-4x^5 - 6x^4 - 9x.
$$
This expression can also be factored by taking $x$ as a common factor:
$$
-4x^5 - 6x^4 - 9x = x(-4x^4 - 6x^3 - 9).
$$
Thus, the simplified answer is
$$
-4x^5 - 6x^4 - 9x \quad \text{or equivalently} \quad x(-4x^4 - 6x^3 - 9).
$$
