Question

question
simplify: \\(\frac{-48x^4 - 24x^2}{6x}\\)

Explanation:

Step1: Split the fraction into two terms

We can split the given fraction \(\frac{-48x^{4}-24x^{2}}{6x}\) into two separate fractions: \(\frac{-48x^{4}}{6x}+\frac{-24x^{2}}{6x}\)

Step2: Simplify each fraction

For the first fraction \(\frac{-48x^{4}}{6x}\), we divide the coefficients and subtract the exponents of \(x\) (using the rule \(\frac{x^{m}}{x^{n}} = x^{m - n}\)):
The coefficient: \(\frac{-48}{6}=-8\)
The exponent of \(x\): \(x^{4-1}=x^{3}\)
So, \(\frac{-48x^{4}}{6x}=-8x^{3}\)

For the second fraction \(\frac{-24x^{2}}{6x}\), we divide the coefficients and subtract the exponents of \(x\):
The coefficient: \(\frac{-24}{6}=-4\)
The exponent of \(x\): \(x^{2 - 1}=x\)
So, \(\frac{-24x^{2}}{6x}=-4x\)

Step3: Combine the simplified terms

Combining the two simplified terms, we get \(-8x^{3}-4x\)

Answer:

\(-8x^{3}-4x\)