Question

find the quotient.
\\(\frac{20x^2y - 88xy}{-4xy}\\)
enter the correct answer.

Explanation:

Step1: Split the fraction

We can split the given fraction \(\frac{20x^{2}y - 88xy}{-4xy}\) into two separate fractions: \(\frac{20x^{2}y}{-4xy}-\frac{88xy}{-4xy}\)

Step2: Simplify the first fraction

For the first fraction \(\frac{20x^{2}y}{-4xy}\), we can simplify the coefficients and the variables separately. The coefficient part: \(\frac{20}{-4}=- 5\), and for the variables, using the rule of exponents \(a^{m}\div a^{n}=a^{m - n}\), we have \(x^{2}\div x=x^{2-1}=x\) and \(y\div y = 1\). So \(\frac{20x^{2}y}{-4xy}=- 5x\)

Step3: Simplify the second fraction

For the second fraction \(\frac{88xy}{-4xy}\), the coefficient part: \(\frac{88}{-4}=- 22\), but we have a negative sign in the denominator and numerator, so \(-\frac{88xy}{-4xy}=\frac{88xy}{4xy}\). The coefficient \(\frac{88}{4} = 22\), and the variables \(x\div x=1\) and \(y\div y = 1\). So \(-\frac{88xy}{-4xy}=22\)

Step4: Combine the results

Combining the results from step 2 and step 3, we get \(-5x + 22\)

Answer:

\(-5x + 22\)