Question

plify: \\(\frac{-48t^4 + 42t^3}{6t}\\)
answer attempt 1 out of 2

Explanation:

Step1: Split the fraction

We can split the given fraction \(\frac{-48t^{4}+42t^{3}}{6t}\) into two separate fractions: \(\frac{-48t^{4}}{6t}+\frac{42t^{3}}{6t}\).

Step2: Simplify each fraction

For the first fraction \(\frac{-48t^{4}}{6t}\), divide the coefficients and subtract the exponents of \(t\) (using the rule \(\frac{a^{m}}{a^{n}} = a^{m - n}\)). The coefficient \(\frac{-48}{6}=-8\) and for the variable part \(\frac{t^{4}}{t}=t^{4 - 1}=t^{3}\), so the first fraction simplifies to \(-8t^{3}\).
For the second fraction \(\frac{42t^{3}}{6t}\), divide the coefficients \(\frac{42}{6} = 7\) and for the variable part \(\frac{t^{3}}{t}=t^{3-1}=t^{2}\), so the second fraction simplifies to \(7t^{2}\).

Step3: Combine the results

Combining the two simplified fractions, we get \(-8t^{3}+7t^{2}\).

Answer:

\(-8t^{3}+7t^{2}\)