Question

find the quotient.
\\(\frac{-30s^3t - 20st}{10st}\\)
enter the correct answer.

Explanation:

Step1: Split the fraction

We can split the given fraction \(\frac{-30s^{3}t - 20st}{10st}\) into two separate fractions: \(\frac{-30s^{3}t}{10st}+\frac{- 20st}{10st}\)

Step2: Simplify the first fraction

For \(\frac{-30s^{3}t}{10st}\), we divide the coefficients and subtract the exponents of like bases. The coefficient \(\frac{-30}{10}=- 3\), for \(s\) we have \(s^{3 - 1}=s^{2}\) (using the rule \(a^{m}/a^{n}=a^{m - n}\)), and for \(t\) we have \(t^{1-1}=t^{0} = 1\). So \(\frac{-30s^{3}t}{10st}=-3s^{2}\)

Step3: Simplify the second fraction

For \(\frac{-20st}{10st}\), the coefficient \(\frac{-20}{10}=-2\), for \(s\) we have \(s^{1 - 1}=s^{0}=1\), and for \(t\) we have \(t^{1-1}=t^{0} = 1\). So \(\frac{-20st}{10st}=-2\)

Step4: Combine the results

Combining the two simplified fractions, we get \(-3s^{2}-2\)

Answer:

\(-3s^{2}-2\)