Question

divide.\\(\frac{24x^5 + 33x^4 + 12x^3}{4x^3}\\)simplify your answer as much as possible.

Explanation:

Step1: Split the fraction

$\frac{24x^5 + 33x^4 + 12x^3}{4x^3} = \frac{24x^5}{4x^3} + \frac{33x^4}{4x^3} + \frac{12x^3}{4x^3}$

Step2: Simplify each term

Simplify coefficients and exponents using $\frac{x^a}{x^b}=x^{a-b}$:
$\frac{24}{4}x^{5-3} + \frac{33}{4}x^{4-3} + \frac{12}{4}x^{3-3}$

Step3: Calculate final terms

$6x^2 + \frac{33}{4}x + 3$

Answer:

$6x^2 + \frac{33}{4}x + 3$