Question

divide.
\\(\frac{ - 16x^5 - 16x^4 - 12x^3}{ - 4x^4}\\)

Explanation:

Step1: Split the fraction

Split the numerator into three separate fractions: $\frac{-16x^5}{-4x^4} + \frac{-16x^4}{-4x^4} + \frac{-12x^3}{-4x^4}$

Step2: Simplify each fraction

For the first fraction: $\frac{-16x^5}{-4x^4} = 4x$ (using $\frac{a^m}{a^n}=a^{m - n}$ and $\frac{-16}{-4}=4$)
For the second fraction: $\frac{-16x^4}{-4x^4} = 4$ (since $\frac{-16}{-4}=4$ and $\frac{x^4}{x^4}=1$)
For the third fraction: $\frac{-12x^3}{-4x^4} = \frac{3}{x}$ (simplify coefficients $\frac{-12}{-4}=3$ and use $\frac{x^3}{x^4}=x^{-1}=\frac{1}{x}$)

Step3: Combine the results

Combine the simplified fractions: $4x + 4 + \frac{3}{x}$

Answer:

$4x + 4 + \frac{3}{x}$