Question

find the quotient. \\(\frac{-92a^2b + 36ab}{4ab}\\) enter the correct answer.

Explanation:

Step1: Split the fraction

We can split the given fraction into two separate fractions:
$$\frac{-92a^{2}b + 36ab}{4ab}=\frac{-92a^{2}b}{4ab}+\frac{36ab}{4ab}$$

Step2: Simplify the first fraction

For the first fraction $\frac{-92a^{2}b}{4ab}$, we can simplify the coefficients and the variables separately. The coefficient simplifies as $\frac{-92}{4}=-23$, and for the variables, using the rule of exponents $a^{m}/a^{n}=a^{m - n}$ and $b^{m}/b^{n}=b^{m - n}$, we have $a^{2}/a=a^{2-1}=a$ and $b/b = 1$. So the first fraction simplifies to $-23a$.

Step3: Simplify the second fraction

For the second fraction $\frac{36ab}{4ab}$, the coefficient simplifies as $\frac{36}{4} = 9$, and the variables $a/a=1$ and $b/b = 1$. So the second fraction simplifies to $9$.

Step4: Combine the results

Combining the results from Step 2 and Step 3, we get:
$$-23a+9$$

Answer:

$-23a + 9$