Question

divide.
\frac{-24x^4 - 30x^3 - 42x^2}{-6x^3}

Explanation:

Step1: Split the fraction

We can split the numerator into three separate fractions over the same denominator:
$$\frac{-24x^4}{-6x^3} + \frac{-30x^3}{-6x^3} + \frac{-42x^2}{-6x^3}$$

Step2: Simplify each fraction

For the first fraction:
Using the rule of exponents $\frac{x^a}{x^b}=x^{a - b}$ and dividing the coefficients:
$\frac{-24}{-6}=4$ and $\frac{x^4}{x^3}=x^{4 - 3}=x$, so the first fraction simplifies to $4x$.
For the second fraction:
$\frac{-30}{-6}=5$ and $\frac{x^3}{x^3}=x^{3 - 3}=x^0 = 1$, so the second fraction simplifies to $5$.
For the third fraction:
$\frac{-42}{-6}=7$ and $\frac{x^2}{x^3}=x^{2 - 3}=x^{-1}=\frac{1}{x}$, so the third fraction simplifies to $\frac{7}{x}$.

Step3: Combine the results

Combining the simplified fractions, we get:
$4x + 5+\frac{7}{x}$

Answer:

$4x + 5+\frac{7}{x}$