what is the quotient?\n$\frac{3y + 2}{3y}div\frac{6y^{2}+4y}{3y + 2}$\n$\frac{1}{2y}$\n$\frac{3y +…

what is the quotient?\n$\frac{3y + 2}{3y}div\frac{6y^{2}+4y}{3y + 2}$\n$\frac{1}{2y}$\n$\frac{3y + 2}{6y^{2}}$\n$\frac{1}{y}$\n$\frac{2(3y + 2)}{3}$

what is the quotient?\n$\frac{3y + 2}{3y}div\frac{6y^{2}+4y}{3y + 2}$\n$\frac{1}{2y}$\n$\frac{3y + 2}{6y^{2}}$\n$\frac{1}{y}$\n$\frac{2(3y + 2)}{3}$

Answer

Explanation:

Step1: Recall division of fractions rule

Dividing by a fraction is multiplying by its reciprocal. So $\frac{3y + 2}{3y}\div\frac{6y^{2}+4y}{3y + 2}=\frac{3y + 2}{3y}\times\frac{3y + 2}{6y^{2}+4y}$.

Step2: Factor the denominator of the second - fraction

Factor out $2y$ from $6y^{2}+4y$, we get $6y^{2}+4y = 2y(3y + 2)$. Then the expression becomes $\frac{3y + 2}{3y}\times\frac{3y + 2}{2y(3y + 2)}$.

Step3: Simplify the expression

Cancel out the common factor $(3y + 2)$ in the numerator and denominator. We have $\frac{3y + 2}{3y}\times\frac{3y + 2}{2y(3y + 2)}=\frac{1}{3y}\times\frac{3y + 2}{2y}=\frac{1}{y}\times\frac{1}{2}=\frac{1}{2y}$.

Answer:

$\frac{1}{2y}$