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Simplify the expression:

\[
(-18xu + 9x^{7}u^{5} + 24x^{7}u^{4}) \div (3x^{3}u^{2})
\]

Simplify your answer as much as possible.

Answer :

The division of these expressions "(-18xu+9x^(7)u^(5)+24x^(7)u^(4))-:(3x^(3)u^(2))" gives the simplified expression "3x^(4)u^(3) + 8x^(4)u^(2) - 6/(x^(2)u)":

To simplify the given expression, we need to divide each term by the divisor 3x^(3)u^(2):(-18xu)/(3x^(3)u^(2)) + (9x^(7)u^(5))/(3x^(3)u^(2)) + (24x^(7)u^(4))/(3x^(3)u^(2))

Simplifying each term by canceling out common factors gives us:

-6/(x^(2)u) + 3x^(4)u^(3) + 8x^(4)u^(2)

Combining like terms gives us the final simplified expression:

3x^(4)u^(3) + 8x^(4)u^(2) - 6/(x^(2)u).

Therefore, the simplified expression is 3x^(4)u^(3) + 8x^(4)u^(2) - 6/(x^(2)u).

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